Itō, Kiyosi 19152008
Overview
Works:  157 works in 690 publications in 6 languages and 9,982 library holdings 

Genres:  Conference papers and proceedings Dictionaries 
Roles:  Author, Editor, Honoree, Publishing director, Dedicatee, Other, ed 
Classifications:  QA273, 519.2 
Publication Timeline
.
Most widely held works about
Kiyosi Itō
 Stochastic analysis and applications : the Abel Symposium 2005 : proceedings of the Second Abel Symposium, Oslo, July 29August 4, 2005, held in honor of Kiyosi Itō by Abel Symposium( )
 Diffusions, Markov processes, and martingales by D Williams( Book )
 Itō's stochastic calculus and probability theory by Nobuyuki Ikeda( Book )
 Wolfgang Doeblin : a mathematician rediscovered by Agnes Handwerk( Visual )
 Markov processes from K. Itô's perspective by Daniel W Stroock( Book )
 Wolfgang Doeblin a mathematician redisocovered.( Visual )
 Internet dans vingt ans : le cyberespace, la nouvelle frontière? by Riel Miller( Book )
more
fewer
Most widely held works by
Kiyosi Itō
Diffusion processes and their sample paths by
Kiyosi Itō(
Book
)
50 editions published between 1965 and 2010 in 3 languages and held by 857 WorldCat member libraries worldwide
"Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one or more dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean."
50 editions published between 1965 and 2010 in 3 languages and held by 857 WorldCat member libraries worldwide
"Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one or more dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean."
Encyclopedic dictionary of mathematics by
Nihon Sūgakkai(
Book
)
18 editions published in 1987 in English and held by 768 WorldCat member libraries worldwide
18 editions published in 1987 in English and held by 768 WorldCat member libraries worldwide
Markov processes from K. Itô's perspective by
Daniel W Stroock(
)
3 editions published in 2003 in English and held by 757 WorldCat member libraries worldwide
Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the KolmogorovFeller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A.N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuoustime, stochastic processes
3 editions published in 2003 in English and held by 757 WorldCat member libraries worldwide
Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the KolmogorovFeller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A.N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuoustime, stochastic processes
Introduction to probability theory by
Kiyosi Itō(
Book
)
30 editions published between 1953 and 1991 in 3 languages and held by 720 WorldCat member libraries worldwide
"Professor Itô is one of the most distinguished probability theorists in the world, and in this modern, concise introduction to the subject he explains basic probabilistic concepts rigorously and yet gives at the same time an intuitive understanding of random phenomena. In the first chapter he considers finite situations, but from an advanced standpoint that enables the transition to greater generality to be achieved more easily. Chapter 2 deals with probability measures and includes a discussion of the fundamental concepts of probability theory. These concepts are formulated abstractly but without sacrificing intuition. The last chapter is devoted to infinite sums of independent real random variables. Each chapter is divided into sections that end with a set of problems with hints for solution. This textbook will be particularly valuable to students of mathematics taking courses in probability theory who need a modern introduction to the subject that yet does not allow overemphasis on abstractness to cloud the issues involved"Publisher's description
30 editions published between 1953 and 1991 in 3 languages and held by 720 WorldCat member libraries worldwide
"Professor Itô is one of the most distinguished probability theorists in the world, and in this modern, concise introduction to the subject he explains basic probabilistic concepts rigorously and yet gives at the same time an intuitive understanding of random phenomena. In the first chapter he considers finite situations, but from an advanced standpoint that enables the transition to greater generality to be achieved more easily. Chapter 2 deals with probability measures and includes a discussion of the fundamental concepts of probability theory. These concepts are formulated abstractly but without sacrificing intuition. The last chapter is devoted to infinite sums of independent real random variables. Each chapter is divided into sections that end with a set of problems with hints for solution. This textbook will be particularly valuable to students of mathematics taking courses in probability theory who need a modern introduction to the subject that yet does not allow overemphasis on abstractness to cloud the issues involved"Publisher's description
Stochastic processes and their applications : proceedings of the international conference held in Nagoya, July 26, 1985 by
Kiyosi Itō(
Book
)
30 editions published between 1986 and 2008 in English and held by 621 WorldCat member libraries worldwide
30 editions published between 1986 and 2008 in English and held by 621 WorldCat member libraries worldwide
Probability theory and mathematical statistics : proceedings of the fourth USSRJapan symposium, held at Tbilisi, USSR, August
2329, 1982 by
Kiyosi Itō(
Book
)
27 editions published between 1983 and 2006 in 3 languages and held by 533 WorldCat member libraries worldwide
27 editions published between 1983 and 2006 in 3 languages and held by 533 WorldCat member libraries worldwide
Foundations of stochastic differential equations in infinite dimensional spaces by
Kiyosi Itō(
Book
)
18 editions published between 1984 and 2002 in English and held by 402 WorldCat member libraries worldwide
A systematic, selfcontained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces
18 editions published between 1984 and 2002 in English and held by 402 WorldCat member libraries worldwide
A systematic, selfcontained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces
Stochastic analysis : proceedings of the Taniguchi International Symposium on Stochastic Analysis, Katata and Kyoto, 1982 by
Kiyosi Itō(
Book
)
26 editions published between 1982 and 1984 in English and Undetermined and held by 398 WorldCat member libraries worldwide
Stochastic analysis, a branch of probability theory stemming from the theory of stochastic differential equations, is becoming increasingly important in connection with partial differential equations, nonlinear functional analysis, control theory and statistical mechanics
26 editions published between 1982 and 1984 in English and Undetermined and held by 398 WorldCat member libraries worldwide
Stochastic analysis, a branch of probability theory stemming from the theory of stochastic differential equations, is becoming increasingly important in connection with partial differential equations, nonlinear functional analysis, control theory and statistical mechanics
Encyclopedic dictionary of mathematics by
Nihon Sūgakkai(
Book
)
17 editions published between 1986 and 2000 in English and held by 351 WorldCat member libraries worldwide
V.1. A.N. v.2. O.Z. Apendices and indexes
17 editions published between 1986 and 2000 in English and held by 351 WorldCat member libraries worldwide
V.1. A.N. v.2. O.Z. Apendices and indexes
Stochastic processes : lectures given at Aarhus University by
Kiyosi Itō(
Book
)
17 editions published between 2000 and 2011 in English and held by 300 WorldCat member libraries worldwide
This introduction to the theory of stochastic processes emphasises processes with independent increments and Markov processes. Two separate Sections present about 70 exercises and their complete solutions
17 editions published between 2000 and 2011 in English and held by 300 WorldCat member libraries worldwide
This introduction to the theory of stochastic processes emphasises processes with independent increments and Markov processes. Two separate Sections present about 70 exercises and their complete solutions
Poisson point processes and their application to Markov processes by
Kiyosi Itō(
)
13 editions published between 2015 and 2016 in English and German and held by 286 WorldCat member libraries worldwide
An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of onedimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a onetoone correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumpingin measure and a nonnegative number m< (called the stagnancy rate). The necessary and sufficient conditions for a pair k, m was obtained so that the correspondenc
13 editions published between 2015 and 2016 in English and German and held by 286 WorldCat member libraries worldwide
An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of onedimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a onetoone correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumpingin measure and a nonnegative number m< (called the stagnancy rate). The necessary and sufficient conditions for a pair k, m was obtained so that the correspondenc
Lectures on stochastic processes by
Kiyosi Itō(
Book
)
22 editions published between 1961 and 1984 in 4 languages and held by 283 WorldCat member libraries worldwide
22 editions published between 1961 and 1984 in 4 languages and held by 283 WorldCat member libraries worldwide
Proceedings of the International Symposium on Stochastic Differential Equations, Kyoto, 1976 by
Kiyosi Itō(
Book
)
16 editions published in 1978 in English and held by 266 WorldCat member libraries worldwide
16 editions published in 1978 in English and held by 266 WorldCat member libraries worldwide
On stochastic differential equations by
Kiyosi Itō(
Book
)
32 editions published between 1951 and 2000 in 3 languages and held by 256 WorldCat member libraries worldwide
32 editions published between 1951 and 2000 in 3 languages and held by 256 WorldCat member libraries worldwide
Kiyosi Itô : selected papers by
Kiyosi Itō(
Book
)
7 editions published between 1986 and 1987 in English and held by 212 WorldCat member libraries worldwide
7 editions published between 1986 and 1987 in English and held by 212 WorldCat member libraries worldwide
Essentials of stochastic processes by
Kiyosi Itō(
Book
)
2 editions published in 2006 in English and held by 206 WorldCat member libraries worldwide
"This book is an English translation of Kiyosi Ito's monography published in Japanese in 1957. It gives a unified and comprehensive account of additive processes (or Levy processes), stationary processes, and Markov processes, which constitute the three most important classes of stochastic processes. Written by one of the leading experts in the field, this volume presents to the reader lucid explanations of the fundamental concepts and basic results in each of these three major areas of the theory of stochastic processes."BOOK JACKET
2 editions published in 2006 in English and held by 206 WorldCat member libraries worldwide
"This book is an English translation of Kiyosi Ito's monography published in Japanese in 1957. It gives a unified and comprehensive account of additive processes (or Levy processes), stationary processes, and Markov processes, which constitute the three most important classes of stochastic processes. Written by one of the leading experts in the field, this volume presents to the reader lucid explanations of the fundamental concepts and basic results in each of these three major areas of the theory of stochastic processes."BOOK JACKET
Stochastic processes, 1968/69 by
Kiyosi Itō(
Book
)
22 editions published between 1957 and 2009 in 3 languages and held by 166 WorldCat member libraries worldwide
22 editions published between 1957 and 2009 in 3 languages and held by 166 WorldCat member libraries worldwide
Exponentially stable approximations of weakly damped wave equations by
H. T Banks(
Book
)
8 editions published in 1991 in English and held by 148 WorldCat member libraries worldwide
We consider wave equations with damping in the boundary conditions. Techniques to ascertain the uniform preservation under approximation of exponential stability are presented. Several schemes for which preservation can be guaranteed are analyzed. Numerical results that demonstrate the lack of stability under approximation for several popular schemes (including standard finite difference and finite element schemes) are given
8 editions published in 1991 in English and held by 148 WorldCat member libraries worldwide
We consider wave equations with damping in the boundary conditions. Techniques to ascertain the uniform preservation under approximation of exponential stability are presented. Several schemes for which preservation can be guaranteed are analyzed. Numerical results that demonstrate the lack of stability under approximation for several popular schemes (including standard finite difference and finite element schemes) are given
Probabilistic methods in mathematical physics : proceedings of the Taniguchi International Symposium, Katata and Kyoto, 1985 by
Kiyosi Itō(
Book
)
11 editions published in 1987 in English and held by 140 WorldCat member libraries worldwide
11 editions published in 1987 in English and held by 140 WorldCat member libraries worldwide
Collected papers by
Kōsaku Yoshida(
Book
)
11 editions published between 1992 and 2014 in 3 languages and held by 133 WorldCat member libraries worldwide
11 editions published between 1992 and 2014 in 3 languages and held by 133 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Nihon Sūgakkai Other
 Stroock, Daniel W. Other Author Editor
 McKean, Henry P. (Henry Pratt) 1930
 Hida, Takeyuki 1927 Other Author Editor
 Prokhorov, I︠U︡. V. (I︠U︡riĭ Vasilʹevich) Author Editor
 Taniguchi K�ogy�o Sh�oreikai
 Benth, Fred Espen 1969 Author Editor
 佐藤, 健一 (1934 ) Editor
 Sato, Keniti 1934 Editor
 Ikeda, Nobuyuki Editor
Useful Links
Associated Subjects
Brownian motion processes Brownian movements Differential equations Diffusion Diffusion processes Distribution (Probability theory) Döblin, Alfred, Doeblin, Wolfgang Engineering mathematics Exponential functions Families Finance France Functional analysis Function spaces Germany Global analysis (Mathematics) Itō, Kiyosi, Kolmogorov, A. N.(Andreĭ Nikolaevich), Markov processes Martingales (Mathematics) Mathematical physics Mathematical statistics Mathematicians Mathematics Measure theory Poisson processes Probabilities Semigroups Statistics Stochastic analysis Stochastic difference equations Stochastic differential equations Stochastic integrals Stochastic processes
Covers
Alternative Names
Itô, K.
Itō, K. 1915
Itō, K. 19152008
Itō, K. (Kiyoshi), 1915
Ito, K. (Kiyosi), 1915
Itô, K., (Kiyosi) 19152008
Itō, Kiesi
Ito, Kiesi 1915
Itō, Kiesi 19152008
Itô, Kiosi 19152008
Itō, Kiyoshi
Ito, Kiyoshi 1915
Itō, Kiyoshi 19152008
Itō Kiyoshi japanischer Mathematiker
Itō, Kiyosi
Itô, Kiyosi 1915
Itō, Kiyosi 19152008
Itō, Kyosi 1915
Kijoši Itó
Kijoŝi Ito japana matematikisto
Kiyoshi Itō Japanese mathematician
Kiyoshi Itō Japans wiskundige (19152008)
Kiyoshi Itō japansk matematiker
Kiyoshi Itō matematico giapponese
Kiyoshi Itō matemático japonés
Kiyoshi Itō mathématicien japonais
Kiyosi Itô.
Ито К.
Ито, К 19152008
Ито, Киёси
Кійосі Іто
קיושי איטו מתמטיקאי יפני
كيوشي إيتو رياضياتي ياباني
کیوشی ایتو ریاضیدان ژاپنی
이토 기요시
イトウ, キヨシ
イトウ, キヨシ 19152008
伊藤, 清
伊藤 清 19152008
伊藤清 19152008
伊藤清 数学者
Languages