Schilling, René L.
Overview
Works:  46 works in 261 publications in 3 languages and 8,491 library holdings 

Genres:  Textbooks 
Roles:  Author, Contributor, Other, dgs, Editor, htt 
Classifications:  QC20.7.M43, 515.42 
Publication Timeline
.
Most widely held works by
René L Schilling
Bernstein functions : theory and applications by
René L Schilling(
)
36 editions published between 2009 and 2012 in English and German and held by 2,442 WorldCat member libraries worldwide
"This text is a selfcontained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided."Jacket
36 editions published between 2009 and 2012 in English and German and held by 2,442 WorldCat member libraries worldwide
"This text is a selfcontained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided."Jacket
Brownian motion : an introduction to stochastic processes by
René L Schilling(
)
34 editions published between 2012 and 2014 in English and held by 1,749 WorldCat member libraries worldwide
Stochastic processes occureverywhere in sciences and engineering, and need to be understood by applied mathematicians, engineers and scientists alike. This isa first course introducing the reader gently to the subject. Brownian motions areastochastic process, central to many applications and easyto treat
34 editions published between 2012 and 2014 in English and held by 1,749 WorldCat member libraries worldwide
Stochastic processes occureverywhere in sciences and engineering, and need to be understood by applied mathematicians, engineers and scientists alike. This isa first course introducing the reader gently to the subject. Brownian motions areastochastic process, central to many applications and easyto treat
Measures, integrals and martingales by
René L Schilling(
)
44 editions published between 2005 and 2018 in English and French and held by 1,201 WorldCat member libraries worldwide
This is a concise and elementary introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability theory. Undergraduate calculus and an introductory course on rigorous analysis in R are the only essential prerequisites, making the text suitable for both lecture courses and for selfstudy. Numerous illustrations and exercises are included to consolidate what has already been learned and to discover variants and extensions to the main material. Hints and solutions will be available on the Internet
44 editions published between 2005 and 2018 in English and French and held by 1,201 WorldCat member libraries worldwide
This is a concise and elementary introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability theory. Undergraduate calculus and an introductory course on rigorous analysis in R are the only essential prerequisites, making the text suitable for both lecture courses and for selfstudy. Numerous illustrations and exercises are included to consolidate what has already been learned and to discover variants and extensions to the main material. Hints and solutions will be available on the Internet
Wahrscheinlichkeit eine Einführung für BachelorStudenten by
René L Schilling(
)
14 editions published between 2016 and 2017 in German and English and held by 1,123 WorldCat member libraries worldwide
Die Wahrscheinlichkeitstheorie gehört zu den Kerndisziplinen der modernen Mathematikausbildung. Sie ist die Grundlage für alle Modelle, die "Risiko" und "Unsicherheit" einbeziehen. Dieses Lehrbuch gibt einen direkten, verlässlichen und modernen Zugang zu den wichtigsten Ergebnissen der mathematischen Wahrscheinlichkeitstheorie. Aufbauend auf dem Band "Maß et Integral" werden zunächst elementare Fragen Wahrscheinlichkeitsverteilungen, Zufallsvariable, Unabhängigkeit, bedingte Wahrscheinlichkeiten und charakteristische Funktionen  bis hin zu einfachen Grenzwertsätzen behandelt. Diese Themen werden dann um das Studium von Summen unabhängiger Zufallsvariablen  Gesetze der Großen Zahlen, NullEinsGesetze, random walks, zentraler Grenzwertsatz von LindebergFeller  ergänzt. Allgemeine bedingte Erwartungen, Anwendungen von charakteristischen Funktionen und eine Einführung in die Theorie unendlich teilbarer Verteilungen und der großen Abweichungen runden die Darstellung ab. In gleicher Ausstattung erscheint der Folgeband "Martingale et Prozesse"
14 editions published between 2016 and 2017 in German and English and held by 1,123 WorldCat member libraries worldwide
Die Wahrscheinlichkeitstheorie gehört zu den Kerndisziplinen der modernen Mathematikausbildung. Sie ist die Grundlage für alle Modelle, die "Risiko" und "Unsicherheit" einbeziehen. Dieses Lehrbuch gibt einen direkten, verlässlichen und modernen Zugang zu den wichtigsten Ergebnissen der mathematischen Wahrscheinlichkeitstheorie. Aufbauend auf dem Band "Maß et Integral" werden zunächst elementare Fragen Wahrscheinlichkeitsverteilungen, Zufallsvariable, Unabhängigkeit, bedingte Wahrscheinlichkeiten und charakteristische Funktionen  bis hin zu einfachen Grenzwertsätzen behandelt. Diese Themen werden dann um das Studium von Summen unabhängiger Zufallsvariablen  Gesetze der Großen Zahlen, NullEinsGesetze, random walks, zentraler Grenzwertsatz von LindebergFeller  ergänzt. Allgemeine bedingte Erwartungen, Anwendungen von charakteristischen Funktionen und eine Einführung in die Theorie unendlich teilbarer Verteilungen und der großen Abweichungen runden die Darstellung ab. In gleicher Ausstattung erscheint der Folgeband "Martingale et Prozesse"
Martingale und Prozesse eine Einführung für BachelorStudenten by
René L Schilling(
)
9 editions published in 2018 in German and English and held by 554 WorldCat member libraries worldwide
This is the third volume of the series "Moderne Stochastik" (Modern Stochastics). As a followup to the volume "Wahrscheinlichkeit" (Probability Theory) it gives an intrdouction to dynamical aspects of probability theory using stochastic processes in discrete time. The first part of the book covers discrete martingales  their convergenc behaviour, optional sampling and stopping, uniform integrability and essential martingale inequalities. The power of martingale techniques is illustrated in the chapters on applications of martingales in classical probability and on the BurkholderDavisGundy inequalities. The second half of the book treats random walks on Zd and Rd, their fluctuation behaviour, recurrence and transience. The last two chapters give a brief introduction to probabilistic potential theory and an outlook of further developments: Brownian motion and Donsker's invariance principle ContentsFair Play Conditional Expectation Martingale Stopping and Localizing Martingale Convergence L2Martingales Uniformly Integrable Martingales Some Classical Results of Probability Elementary Inequalities for Martingales The Burkholder{u2013}Davis{u2013}Gundy Inequalities Random Walks on {u2124}d {u2013} the first steps Fluctuations of Simple Random Walks on ZRecurrence and Transience of General Random WalksRandom Walks and AnalysisDonsker's Invariance Principle and Brownian Motion
9 editions published in 2018 in German and English and held by 554 WorldCat member libraries worldwide
This is the third volume of the series "Moderne Stochastik" (Modern Stochastics). As a followup to the volume "Wahrscheinlichkeit" (Probability Theory) it gives an intrdouction to dynamical aspects of probability theory using stochastic processes in discrete time. The first part of the book covers discrete martingales  their convergenc behaviour, optional sampling and stopping, uniform integrability and essential martingale inequalities. The power of martingale techniques is illustrated in the chapters on applications of martingales in classical probability and on the BurkholderDavisGundy inequalities. The second half of the book treats random walks on Zd and Rd, their fluctuation behaviour, recurrence and transience. The last two chapters give a brief introduction to probabilistic potential theory and an outlook of further developments: Brownian motion and Donsker's invariance principle ContentsFair Play Conditional Expectation Martingale Stopping and Localizing Martingale Convergence L2Martingales Uniformly Integrable Martingales Some Classical Results of Probability Elementary Inequalities for Martingales The Burkholder{u2013}Davis{u2013}Gundy Inequalities Random Walks on {u2124}d {u2013} the first steps Fluctuations of Simple Random Walks on ZRecurrence and Transience of General Random WalksRandom Walks and AnalysisDonsker's Invariance Principle and Brownian Motion
Levy matters III : Levytype processes : construction, approximation and sample path properties by
Björn Böttcher(
)
19 editions published between 2013 and 2014 in English and held by 433 WorldCat member libraries worldwide
This volume presents recent developments in the area of Lévytype processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévytype process: a nonrandom function which is?the counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levytype processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the nonBrownian world
19 editions published between 2013 and 2014 in English and held by 433 WorldCat member libraries worldwide
This volume presents recent developments in the area of Lévytype processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévytype process: a nonrandom function which is?the counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levytype processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the nonBrownian world
From LévyType Processes to Parabolic SPDEs by
Davar Khoshnevisan(
)
16 editions published between 2016 and 2017 in English and German and held by 297 WorldCat member libraries worldwide
This volume presents the lecture notes from two courses given by Davar Khoshnevisan and Ren ̌Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis. Ren ̌Schilling's notes are an expanded version of his course on Lv̌y and Lv̌ytype processes, the purpose of which is twofold: on the one hand, the course presents in detail selected properties of the Lv̌y processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Lv̌yIt ̥decomposition. On the other, it identifies the infinitesimal generator of the Lv̌y process as a pseudodifferential operator whose symbol is the characteristic exponent of the process, making it possible to study the properties of Feller processes as space inhomogeneous processes that locally behave like Lv̌y processes. The presentation is selfcontained, and includes dedicated chapters that review Markov processes, operator semigroups, random measures, etc. In turn, Davar Khoshnevisan's course investigates selected problems in the field of stochastic partial differential equations of parabolic type. More precisely, the main objective is to establish an Invariance Principle for those equations in a rather general setting, and to deduce, as an application, comparisontype results. The framework in which these problems are addressed goes beyond the classical setting, in the sense that the driving noise is assumed to be a multiplicative spacetime white noise on a group, and the underlying elliptic operator corresponds to a generator of a Lv̌y process on that group. This implies that stochastic integration with respect to the above noise, as well as the existence and uniqueness of a solution for the corresponding equation, become relevant in their own right. These aspects are also developed and supplemented by a wealth of illustrative examples
16 editions published between 2016 and 2017 in English and German and held by 297 WorldCat member libraries worldwide
This volume presents the lecture notes from two courses given by Davar Khoshnevisan and Ren ̌Schilling, respectively, at the second Barcelona Summer School on Stochastic Analysis. Ren ̌Schilling's notes are an expanded version of his course on Lv̌y and Lv̌ytype processes, the purpose of which is twofold: on the one hand, the course presents in detail selected properties of the Lv̌y processes, mainly as Markov processes, and their different constructions, eventually leading to the celebrated Lv̌yIt ̥decomposition. On the other, it identifies the infinitesimal generator of the Lv̌y process as a pseudodifferential operator whose symbol is the characteristic exponent of the process, making it possible to study the properties of Feller processes as space inhomogeneous processes that locally behave like Lv̌y processes. The presentation is selfcontained, and includes dedicated chapters that review Markov processes, operator semigroups, random measures, etc. In turn, Davar Khoshnevisan's course investigates selected problems in the field of stochastic partial differential equations of parabolic type. More precisely, the main objective is to establish an Invariance Principle for those equations in a rather general setting, and to deduce, as an application, comparisontype results. The framework in which these problems are addressed goes beyond the classical setting, in the sense that the driving noise is assumed to be a multiplicative spacetime white noise on a group, and the underlying elliptic operator corresponds to a generator of a Lv̌y process on that group. This implies that stochastic integration with respect to the above noise, as well as the existence and uniqueness of a solution for the corresponding equation, become relevant in their own right. These aspects are also developed and supplemented by a wealth of illustrative examples
Maß und Integral eine Einführung für BachelorStudenten by
René L Schilling(
)
11 editions published between 2015 and 2016 in German and English and held by 176 WorldCat member libraries worldwide
Many areas of mathematics and their application in physics, economics, and computer science require a firm grasp of measure theory. This textbook provides a concise, reliable, and accurate introduction to the most important elements of measure theory. René Schilling, Technische Universität Dresden
11 editions published between 2015 and 2016 in German and English and held by 176 WorldCat member libraries worldwide
Many areas of mathematics and their application in physics, economics, and computer science require a firm grasp of measure theory. This textbook provides a concise, reliable, and accurate introduction to the most important elements of measure theory. René Schilling, Technische Universität Dresden
Counterexamples in measure and integration by
René L Schilling(
)
9 editions published in 2021 in English and held by 115 WorldCat member libraries worldwide
"Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples  some of them both surprising and amusing  showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a selfcontained, nontechnical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for selfstudy as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales"
9 editions published in 2021 in English and held by 115 WorldCat member libraries worldwide
"Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples  some of them both surprising and amusing  showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a selfcontained, nontechnical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for selfstudy as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales"
Brownian Motion : A Guide to Random Processes and Stochastic Calculus by
René L Schilling(
)
7 editions published in 2021 in English and held by 79 WorldCat member libraries worldwide
Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many reallife models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''
7 editions published in 2021 in English and held by 79 WorldCat member libraries worldwide
Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many reallife models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''
Lévytype processes : construction, approximation and sample path properties by
Björn Böttcher(
Book
)
6 editions published in 2013 in English and held by 40 WorldCat member libraries worldwide
This volume presents recent developments in the area of Lévytype processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévytype process: a nonrandom function which is the counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levytype processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the nonBrownian world
6 editions published in 2013 in English and held by 40 WorldCat member libraries worldwide
This volume presents recent developments in the area of Lévytype processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévytype process: a nonrandom function which is the counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levytype processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the nonBrownian world
Selected papers by
William Feller(
Book
)
4 editions published in 2015 in English and held by 30 WorldCat member libraries worldwide
"These volumes contain a selection of William Feller's most important works on probability theory, mathematical biology, analysis and geometry...The papers are arranged in chronological order: Volume 1 covers the years 19281950, and Volume 2 the period 19511971"
4 editions published in 2015 in English and held by 30 WorldCat member libraries worldwide
"These volumes contain a selection of William Feller's most important works on probability theory, mathematical biology, analysis and geometry...The papers are arranged in chronological order: Volume 1 covers the years 19281950, and Volume 2 the period 19511971"
Prozesse und Martingale by
René L Schilling(
Book
)
1 edition published in 2017 in German and held by 28 WorldCat member libraries worldwide
1 edition published in 2017 in German and held by 28 WorldCat member libraries worldwide
Lévy Matters. LévyType Processes: Construction, Approximation and Sample Path Properties by
Björn Böttcher(
)
1 edition published in 2013 in English and held by 27 WorldCat member libraries worldwide
This volume presents recent developments in the area of Lévytype processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévytype process: a nonrandom function which is the counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levytype processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the nonBrownian world
1 edition published in 2013 in English and held by 27 WorldCat member libraries worldwide
This volume presents recent developments in the area of Lévytype processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévytype process: a nonrandom function which is the counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Levytype processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the nonBrownian world
Zum Pfadverhalten von Markovschen Prozessen, die mit LévyProzessen vergleichbar sind by
René L Schilling(
Book
)
5 editions published in 1994 in German and Undetermined and held by 27 WorldCat member libraries worldwide
5 editions published in 1994 in German and Undetermined and held by 27 WorldCat member libraries worldwide
Function spaces related to continuous negative definite functions : [psi]Bessel potential spaces by
Walter Farkas(
Book
)
3 editions published in 2001 in English and held by 22 WorldCat member libraries worldwide
3 editions published in 2001 in English and held by 22 WorldCat member libraries worldwide
Probability and Heat Kernel Estimates for Lévy(Type) Processes by
Franziska Kühn(
)
2 editions published in 2016 in English and held by 19 WorldCat member libraries worldwide
2 editions published in 2016 in English and held by 19 WorldCat member libraries worldwide
Martingale und Prozesse by
René L Schilling(
)
1 edition published in 2018 in German and held by 17 WorldCat member libraries worldwide
1 edition published in 2018 in German and held by 17 WorldCat member libraries worldwide
LévyType Processes under Uncertainty and Related Nonlocal Equations by
Julian Hollender(
)
1 edition published in 2016 in English and held by 17 WorldCat member libraries worldwide
1 edition published in 2016 in English and held by 17 WorldCat member libraries worldwide
SELECTED PAPERS I by
William Feller(
)
3 editions published in 2015 in English and held by 16 WorldCat member libraries worldwide
"Volume 1 covers the years 19281950, and Volume 2 the period 19511971"
3 editions published in 2015 in English and held by 16 WorldCat member libraries worldwide
"Volume 1 covers the years 19281950, and Volume 2 the period 19511971"
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Related Identities
 Vondraček, Zoran 1959 Author Editor
 Song, Renming 1963 Author
 Böttcher, Björn Other Author Contributor
 Partzsch, Lothar 1945 Author Contributor
 Wang, Jian (Mathematician)
 Khoshnevisan, Davar Author
 Utzet, Frederic Other Editor
 QuerSardanyons, Lluis Other Editor
 Walter de Gruyter GmbH & Co. KG Publisher
 Kühn, Franziska 1989 Author
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Associated Subjects
Algebraic topology Analytic functions Biomathematics Branching processes Brownian motion processes Differential equations, Partial Dirichlet forms Distribution (Probability theory) Functional analysis Functions, Continuous Function spaces Geometry Integrals Lévy processes Martingales (Mathematics) Mathematical analysis Mathematics Measure theory Monotonic functions Operator theory Potential theory (Mathematics) Probabilities Quasianalytic functions Random walks (Mathematics) Sample path analysis Stochastic analysis Stochastic partial differential equations Stochastic processes Trees (Graph theory)