Shiri︠a︡ev, Alʹbert Nikolaevich
Overview
Works:  190 works in 713 publications in 3 languages and 10,109 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Honoree, Adapter, Creator 
Classifications:  QA274, 519.5 
Publication Timeline
.
Most widely held works by
Alʹbert Nikolaevich Shiri︠a︡ev
Probability by
Alʹbert Nikolaevich Shiri︠a︡ev(
Book
)
35 editions published between 1984 and 2010 in 3 languages and held by 893 WorldCat member libraries worldwide
This new edition contains substantial revisions and updated references. The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures. Proofs for a number of some important results which were merely stated in the first edition have been added. The author has included new material on the probability of large deviations, on the central limit theorem for sums of dependent random variables, and on a discrete version of Ito's formula
35 editions published between 1984 and 2010 in 3 languages and held by 893 WorldCat member libraries worldwide
This new edition contains substantial revisions and updated references. The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures. Proofs for a number of some important results which were merely stated in the first edition have been added. The author has included new material on the probability of large deviations, on the central limit theorem for sums of dependent random variables, and on a discrete version of Ito's formula
Statistics of random processes by
R. Sh Lipt︠s︡er(
Book
)
46 editions published between 1977 and 2010 in English and Undetermined and held by 716 WorldCat member libraries worldwide
A considerable number of problems in the statistics of random processes are formulated within the following scheme. On a certain probability space (Q, ff, P) a partially observable random process (lJ,~) = (lJ ~/), t :;::: 0, is given with only the second component n ~ = (~/), t:;::: 0, observed. At any time t it is required, based on ~h = g., s sst}, to estimate the unobservable state lJ/. This problem of estimating (in other words, the filtering problem) 0/ from ~h will be discussed in this book. It is well known that if M(lJ;) < 00, then the optimal mean square esti mate of lJ/ from ~h is the a posteriori mean m/ = M(lJ/1 ff~), where ff~ = CT{ w: ~., sst} is the CTalgebra generated by ~h. Therefore, the solution of the problem of optimal (in the mean square sense) filtering is reduced to finding the conditional (mathematical) expectation m/ = M(lJ/lffa. In principle, the conditional expectation M(lJ/lff;) can be computed by Bayes' formula. However, even in many rather simple cases, equations obtained by Bayes' formula are too cumbersome, and present difficulties in their practical application as well as in the investigation of the structure and properties of the solution
46 editions published between 1977 and 2010 in English and Undetermined and held by 716 WorldCat member libraries worldwide
A considerable number of problems in the statistics of random processes are formulated within the following scheme. On a certain probability space (Q, ff, P) a partially observable random process (lJ,~) = (lJ ~/), t :;::: 0, is given with only the second component n ~ = (~/), t:;::: 0, observed. At any time t it is required, based on ~h = g., s sst}, to estimate the unobservable state lJ/. This problem of estimating (in other words, the filtering problem) 0/ from ~h will be discussed in this book. It is well known that if M(lJ;) < 00, then the optimal mean square esti mate of lJ/ from ~h is the a posteriori mean m/ = M(lJ/1 ff~), where ff~ = CT{ w: ~., sst} is the CTalgebra generated by ~h. Therefore, the solution of the problem of optimal (in the mean square sense) filtering is reduced to finding the conditional (mathematical) expectation m/ = M(lJ/lffa. In principle, the conditional expectation M(lJ/lff;) can be computed by Bayes' formula. However, even in many rather simple cases, equations obtained by Bayes' formula are too cumbersome, and present difficulties in their practical application as well as in the investigation of the structure and properties of the solution
Limit theorems for stochastic processes by
Jean Jacod(
Book
)
27 editions published between 1987 and 2013 in English and Russian and held by 708 WorldCat member libraries worldwide
Proposes a systematic exposition of convergence in law for stochastic processes from the point of view of semimartingale theory. This book emphasizes results that are useful for mathematical theory and mathematical statistics
27 editions published between 1987 and 2013 in English and Russian and held by 708 WorldCat member libraries worldwide
Proposes a systematic exposition of convergence in law for stochastic processes from the point of view of semimartingale theory. This book emphasizes results that are useful for mathematical theory and mathematical statistics
Optimal stopping rules by
Alʹbert Nikolaevich Shiri︠a︡ev(
Book
)
49 editions published between 1969 and 2008 in 3 languages and held by 509 WorldCat member libraries worldwide
Although three decades have passed since first publication of this book reprinted now as a result of popular demand, the content remains uptodate and interesting for many researchers as is shown by the many references to it in current publications. The "ground floor" of Optimal Stopping Theory was constructed by A.Wald in his sequential analysis in connection with the testing of statistical hypotheses by nontraditional (sequential) methods. It was later discovered that these methods have, in idea, a close connection to the general theory of stochastic optimization for random processes. The area of application of the Optimal Stopping Theory is very broad. It is sufficient at this point to emphasise that its methods are well tailored to the study of American (type) options (in mathematics of finance and financial engineering), where a buyer has the freedom to exercise an option at any stopping time. In this book, the general theory of the construction of optimal stopping policies is developed for the case of Markov processes in discrete and continuous time. One chapter is devoted specially to the applications that address problems of the testing of statistical hypotheses, and quickest detection of the time of change of the probability characteristics of the observable processes. The author, A.N.Shiryaev, is one of the leading experts of the field and gives an authoritative treatment of a subject that, 30 years after original publication of this book, is proving increasingly important
49 editions published between 1969 and 2008 in 3 languages and held by 509 WorldCat member libraries worldwide
Although three decades have passed since first publication of this book reprinted now as a result of popular demand, the content remains uptodate and interesting for many researchers as is shown by the many references to it in current publications. The "ground floor" of Optimal Stopping Theory was constructed by A.Wald in his sequential analysis in connection with the testing of statistical hypotheses by nontraditional (sequential) methods. It was later discovered that these methods have, in idea, a close connection to the general theory of stochastic optimization for random processes. The area of application of the Optimal Stopping Theory is very broad. It is sufficient at this point to emphasise that its methods are well tailored to the study of American (type) options (in mathematics of finance and financial engineering), where a buyer has the freedom to exercise an option at any stopping time. In this book, the general theory of the construction of optimal stopping policies is developed for the case of Markov processes in discrete and continuous time. One chapter is devoted specially to the applications that address problems of the testing of statistical hypotheses, and quickest detection of the time of change of the probability characteristics of the observable processes. The author, A.N.Shiryaev, is one of the leading experts of the field and gives an authoritative treatment of a subject that, 30 years after original publication of this book, is proving increasingly important
Essentials of stochastic finance : facts, models, theory by
Alʹbert Nikolaevich Shiri︠a︡ev(
Book
)
47 editions published between 1998 and 2012 in English and held by 446 WorldCat member libraries worldwide
Annotation
47 editions published between 1998 and 2012 in English and held by 446 WorldCat member libraries worldwide
Annotation
Statistical sequential analysis; optimal stopping rules by
Alʹbert Nikolaevich Shiri︠a︡ev(
Book
)
12 editions published in 1973 in English and Undetermined and held by 327 WorldCat member libraries worldwide
Markov times and random processes; Optimal stopping of Markov random sequences; Optimal stopping of markov random processes; Some applications to problems in mathematical statistics
12 editions published in 1973 in English and Undetermined and held by 327 WorldCat member libraries worldwide
Markov times and random processes; Optimal stopping of Markov random sequences; Optimal stopping of markov random processes; Some applications to problems in mathematical statistics
Probability theory by
I︠U︡. V Prokhorov(
Book
)
10 editions published in 1998 in English and held by 250 WorldCat member libraries worldwide
This volume of the Encyclopaedia is a survey of stochastic calculus which has become an increasingly important part of probability. The topics covered include Brownian motion, the Ito integral, stochastic differential equations and Malliavin calculus, the general theory of random processes and martingale theory. The five authors are wellknown experts in the field. The first chapter of the book is an introduction which treats Brownian motion and describes the developments which lead to the definition of Ito's integral. The book addresses graduate students and researchers in probability theory and mathematical statistics and will also be used by physicists and engineers who need to apply stochastic methods
10 editions published in 1998 in English and held by 250 WorldCat member libraries worldwide
This volume of the Encyclopaedia is a survey of stochastic calculus which has become an increasingly important part of probability. The topics covered include Brownian motion, the Ito integral, stochastic differential equations and Malliavin calculus, the general theory of random processes and martingale theory. The five authors are wellknown experts in the field. The first chapter of the book is an introduction which treats Brownian motion and describes the developments which lead to the definition of Ito's integral. The book addresses graduate students and researchers in probability theory and mathematical statistics and will also be used by physicists and engineers who need to apply stochastic methods
Optimal stopping and freeboundary problems by
G Peskir(
Book
)
21 editions published in 2006 in English and held by 236 WorldCat member libraries worldwide
Covers a connection between optimal stopping and freeboundary problems. This book uses minimal tools and focuses on key examples. It exposes the general theory of optimal stopping, at its basic principles in both discrete and continuous time. It is useful for graduate and postgraduate students, researchers, and practitioners
21 editions published in 2006 in English and held by 236 WorldCat member libraries worldwide
Covers a connection between optimal stopping and freeboundary problems. This book uses minimal tools and focuses on key examples. It exposes the general theory of optimal stopping, at its basic principles in both discrete and continuous time. It is useful for graduate and postgraduate students, researchers, and practitioners
Theory of martingales by
R. Sh Lipt︠s︡er(
Book
)
16 editions published between 1986 and 1989 in 3 languages and held by 205 WorldCat member libraries worldwide
One service mathematics has rc:ndered the 'Et moi, "', si j'avait su comment CD revenir, je n'y serais point alle. ' human race. It has put common SCIIJC back Jules Verne where it belongs. on the topmost shelf next to tbe dusty canister 1abdled 'discarded non The series is divergent; tberefore we may be sense'. able to do sometbing witb it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . . . '; 'One service logic has rendered com puter science . . . '; 'One service category theory has rendered mathematics . . . '. All arguably true_ And all statements obtainable this way form part of the raison d'etre of this series_ This series, Mathematics and Its ApplicatiOns, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope_ At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches
16 editions published between 1986 and 1989 in 3 languages and held by 205 WorldCat member libraries worldwide
One service mathematics has rc:ndered the 'Et moi, "', si j'avait su comment CD revenir, je n'y serais point alle. ' human race. It has put common SCIIJC back Jules Verne where it belongs. on the topmost shelf next to tbe dusty canister 1abdled 'discarded non The series is divergent; tberefore we may be sense'. able to do sometbing witb it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics . . . '; 'One service logic has rendered com puter science . . . '; 'One service category theory has rendered mathematics . . . '. All arguably true_ And all statements obtainable this way form part of the raison d'etre of this series_ This series, Mathematics and Its ApplicatiOns, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope_ At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches
Statistics and control of stochastic processes by
Steklov Seminar(
Book
)
5 editions published in 1985 in English and held by 196 WorldCat member libraries worldwide
5 editions published in 1985 in English and held by 196 WorldCat member libraries worldwide
Stochastic optimization : proceedings of the international conference, Kiev, 1984 by
V. I Arkin(
Book
)
6 editions published between 1985 and 1986 in English and held by 190 WorldCat member libraries worldwide
6 editions published between 1985 and 1986 in English and held by 190 WorldCat member libraries worldwide
Contiguity and the statistical invariance principle by
P. E Greenwood(
Book
)
9 editions published between 1985 and 1992 in English and held by 188 WorldCat member libraries worldwide
9 editions published between 1985 and 1992 in English and held by 188 WorldCat member libraries worldwide
Change of time and change of measure by
O. E BarndorffNielsen(
Book
)
11 editions published between 2010 and 2015 in English and held by 150 WorldCat member libraries worldwide
A comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law. The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results
11 editions published between 2010 and 2015 in English and held by 150 WorldCat member libraries worldwide
A comprehensive account of two topics that are of particular significance in both theoretical and applied stochastics: random change of time and change of probability law. The book comprehensively collects and integrates results from a number of scattered sources in the literature and discusses the importance of the results
Statistical experiments and decisions : asymptotic theory by
Alʹbert Nikolaevich Shiri︠a︡ev(
Book
)
9 editions published in 2000 in English and held by 149 WorldCat member libraries worldwide
This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is "how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment."
9 editions published in 2000 in English and held by 149 WorldCat member libraries worldwide
This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is "how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment."
Stochastic finance by
Alʹbert Nikolaevich Shiri︠a︡ev(
Book
)
13 editions published in 2006 in English and held by 141 WorldCat member libraries worldwide
"Mathematics, as the language of science, has always played a role in the development of knowledge and technology. Presently, the hightech character of modern business has increased the need for advanced methods, which rely to a large extent on mathematical techniques. It has become essential for the financial analyst to possess a high degree of proficiency in these mathematical techniques. The essays in Stochastic Finance describe many of these techniques. This book is intended for experts in mathematics, statistics, mathematical finance, and economics."Jacket
13 editions published in 2006 in English and held by 141 WorldCat member libraries worldwide
"Mathematics, as the language of science, has always played a role in the development of knowledge and technology. Presently, the hightech character of modern business has increased the need for advanced methods, which rely to a large extent on mathematical techniques. It has become essential for the financial analyst to possess a high degree of proficiency in these mathematical techniques. The essays in Stochastic Finance describe many of these techniques. This book is intended for experts in mathematics, statistics, mathematical finance, and economics."Jacket
Statistics and control of random processes(
Book
)
3 editions published between 1994 and 1995 in English and held by 129 WorldCat member libraries worldwide
3 editions published between 1994 and 1995 in English and held by 129 WorldCat member libraries worldwide
From stochastic calculus to mathematical finance : the Shiryaev Festschrift by
Yuri Kabanov(
Book
)
7 editions published in 2006 in English and held by 118 WorldCat member libraries worldwide
7 editions published in 2006 in English and held by 118 WorldCat member libraries worldwide
Problems in probability by
Alʹbert Nikolaevich Shiri︠a︡ev(
Book
)
12 editions published in 2012 in English and held by 115 WorldCat member libraries worldwide
Problems in Probability comprises one of the most comprehensive, nearly encyclopedic, collections of problems and exercises in probability theory. Albert Shiryaev has skillfully created, collected, and compiled the exercises in this text over the course of many years while working on topics which interested him the most. A substantial number of the exercises resulted from diverse sources such as textbooks, lecture notes, exercise manuals, monographs, and discussions that took place during special seminars for graduate and undergraduate students. Many problems contain helpful hints and other relevant comments and a portion of the material covers some important applications from optimal control and mathematical finance. Readers of diverse backgroundsfrom students to researcherswill find a great deal of value in this book and can treat the work as an exercise manual, a handbook, or as a supplementary text to a course in probability theory, control, and mathematical finance. The problems and exercises in this book vary in nature and degree of difficulty. Some problems are meant to test the reader's basic understanding, others are of mediumtohigh degrees of difficulty and require more creative thinking. Other problems are meant to develop additional theoretical concepts and tools or to familiarize the reader with various facts that are not necessarily covered in mainstream texts. Additional problems are related to the passage from random walk to Brownian motions and Brownian bridges. The appendix contains a summary of the main results, notation and terminology that are used throughout the book. It also contains additional material from combinatorics, potential theory and Markov chainssubjects that are not covered in the book, but are nevertheless needed for many of the exercises included here
12 editions published in 2012 in English and held by 115 WorldCat member libraries worldwide
Problems in Probability comprises one of the most comprehensive, nearly encyclopedic, collections of problems and exercises in probability theory. Albert Shiryaev has skillfully created, collected, and compiled the exercises in this text over the course of many years while working on topics which interested him the most. A substantial number of the exercises resulted from diverse sources such as textbooks, lecture notes, exercise manuals, monographs, and discussions that took place during special seminars for graduate and undergraduate students. Many problems contain helpful hints and other relevant comments and a portion of the material covers some important applications from optimal control and mathematical finance. Readers of diverse backgroundsfrom students to researcherswill find a great deal of value in this book and can treat the work as an exercise manual, a handbook, or as a supplementary text to a course in probability theory, control, and mathematical finance. The problems and exercises in this book vary in nature and degree of difficulty. Some problems are meant to test the reader's basic understanding, others are of mediumtohigh degrees of difficulty and require more creative thinking. Other problems are meant to develop additional theoretical concepts and tools or to familiarize the reader with various facts that are not necessarily covered in mainstream texts. Additional problems are related to the passage from random walk to Brownian motions and Brownian bridges. The appendix contains a summary of the main results, notation and terminology that are used throughout the book. It also contains additional material from combinatorics, potential theory and Markov chainssubjects that are not covered in the book, but are nevertheless needed for many of the exercises included here
Statistics of Random processes II : Applications by
R. Sh Lipt︠s︡er(
Book
)
10 editions published between 1974 and 2001 in English and Undetermined and held by 31 WorldCat member libraries worldwide
The subject of these two volumes is nonlinear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The required mathematical background is presented in the first volume: the theory of martingales, stochastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of stochastic calculus for counting processes. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years
10 editions published between 1974 and 2001 in English and Undetermined and held by 31 WorldCat member libraries worldwide
The subject of these two volumes is nonlinear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The required mathematical background is presented in the first volume: the theory of martingales, stochastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of stochastic calculus for counting processes. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years
Prokhorov and contemporary probability theory : in honor of Yuri V. Prokhorov by
Alʹbert Nikolaevich Shiri︠a︡ev(
Book
)
8 editions published between 2012 and 2015 in English and held by 2 WorldCat member libraries worldwide
The role of Yuri Vasilyevich Prokhorov as a prominent mathematician and leading expert in the theory of probability is well known. Even early in his career he obtained substantial results on the validity of the strong law of large numbers and on the estimates (bounds) of the rates of convergence, some of which are the best possible. His findings on limit theorems in metric spaces and particularly functional limit theorems are of exceptional importance. Y.V. Prokhorov developed an original approach to the proof of functional limit theorems, based on the weak convergence of finite dimensional di
8 editions published between 2012 and 2015 in English and held by 2 WorldCat member libraries worldwide
The role of Yuri Vasilyevich Prokhorov as a prominent mathematician and leading expert in the theory of probability is well known. Even early in his career he obtained substantial results on the validity of the strong law of large numbers and on the estimates (bounds) of the rates of convergence, some of which are the best possible. His findings on limit theorems in metric spaces and particularly functional limit theorems are of exceptional importance. Y.V. Prokhorov developed an original approach to the proof of functional limit theorems, based on the weak convergence of finite dimensional di
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Related Identities
 Lipt︠s︡er, R. Sh (Robert Shevilevich) Author
 Jacod, Jean Author
 Aries, A. B. Translator
 Peskir, G. (Goran) Other Author
 Kabanov, Yuri Author
 Stoi︠a︡nov, Ĭordan
 Varadhan, S. R. S. Editor
 Presman, Ė. L. (Ėrnst Lʹvovich) Editor
 Novikov, A. A. mathematician
 Prokhorov, I︠U︡. V. (I︠U︡riĭ Vasilʹevich) Author Editor
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Associated Subjects
Asymptotic expansions Boundary value problems Business mathematics Combinatorial analysis Computer engineering Continuity Control theory Differential equations, Partial Distribution (Probability theory) Economics Economics, Mathematical Engineering Experimental design Finance FinanceMathematical models Financial engineering InvestmentsMathematics Limit theorems (Probability theory) Markov processes Martingales (Mathematics) Mathematical optimization Mathematical statistics Mathematics Measure theory Nonlinear integral equations Optimal stopping (Mathematical statistics) Probabilities Quantum theory Random measures Semimartingales (Mathematics) Sequential analysis Statistical decision Statistics Stochastic analysis Stochastic models Stochastic processes Timeseries analysis
Alternative Names
Albert Nikolajewitsch Schirjajew russischer Mathematiker
Albert Shiryaev mathmaticien russe
Albert Shiryaev Russian mathematician
Chiriaev Albert Nikolaevitch 1934....
Shiri︠a︡ev, A. N.
Shiri︠a︡ev, A. N. 1934
Shiri︠a︡ev, A. N. (Alʹbert Nikolaevich)
Shiri︠a︡ev, A. N. (Alʹbert Nikolaevich), 1934
Shiriaev, Al'bert N. 1934
Shiri︠a︡ev, Alʹbert Nikolaevich
Shiri︠a︡ev, Alʹbert Nikolaevich 1934
Šhirjaev, A. N. 1934
Shiryaev, A. N.
Shiryaev, A.N. 1934
Shiryaev, Albert.
Shiryaev, Albert 1934
Shiryaev, Albert N.
Shiryaev, Albert N. 1934...
Shiryaev Albert Nicolaevich 1934....
Shiryaev, Albert Nikolaevich 1934
Shiryayev, A. N.
Shiryayev, A.N. 1934
Shiryayev, Albert N. 1934
Shiryayev, Albert Nikolaevich
Shiryayev Albert Nikolaevich 1934....
Shyriaev, A.N.
Shyriaev, A.N. (Albert Nicolaevitch)
Shyriaev, Albert N. 1934
Širev, A. N.
Širev, Alʹbert Nikolaevič 1934...
Širjaev, A. N.
Širjaev, A. N. 1934
Širjaev, Albert
Širjaev, Al'bert N. 1934
Širjaev, Al'bert Nikolaevič
Širjaev, Al'bert Nikolaevič 1934
Širjaev, Al'bert Nikolaevič. [t]
Širjajev, Alʹbert Nikolaevič 1934
Sjirjajew 1934
Sziriajew, A. N.
Ширяев, А. Н
Ширяев, А. Н. (Альберт Николаевич)
Ширяев, Альберт Николаевич.
Ширяев Альберт Николаевич 1934....
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