Dynkin, E. B. (Evgeniĭ Borisovich) 19242014
Overview
Works:  119 works in 625 publications in 5 languages and 7,587 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Honoree, Editor, Other 
Classifications:  QA273, 519.1 
Publication Timeline
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Most widely held works about
E. B Dynkin
 Eugene B. Dynkin Collection of Mathematics Interviews by E. B Dynkin( )
Most widely held works by
E. B Dynkin
Markov processes by
E. B Dynkin(
Book
)
24 editions published in 1965 in 3 languages and held by 583 WorldCat member libraries worldwide
24 editions published in 1965 in 3 languages and held by 583 WorldCat member libraries worldwide
Theory of Markov processes by
E. B Dynkin(
Book
)
40 editions published between 1959 and 2012 in 3 languages and held by 517 WorldCat member libraries worldwide
Cover; Title Page; Copyright Page; Contents; Preface; THEORY OF MARKOV PROCESSES; Chapter 1  Introduction; 1. Measurable spaces and measurable sets; 2. Measures and intergrals; 3. Conditional probabilities and mathematical expectations; 4. Topological measurable spaces; 5. The construction of probability measures; Chapter 2  Markov Processes; 1. The definition of Markov processes; 2. Stationary Markov processes; 3. Equivalent of Markov processes; Chapter 3  Subprocesses; 1. The definition of Subprocesses. The connexion between subprocesses and multiplicative functionals
40 editions published between 1959 and 2012 in 3 languages and held by 517 WorldCat member libraries worldwide
Cover; Title Page; Copyright Page; Contents; Preface; THEORY OF MARKOV PROCESSES; Chapter 1  Introduction; 1. Measurable spaces and measurable sets; 2. Measures and intergrals; 3. Conditional probabilities and mathematical expectations; 4. Topological measurable spaces; 5. The construction of probability measures; Chapter 2  Markov Processes; 1. The definition of Markov processes; 2. Stationary Markov processes; 3. Equivalent of Markov processes; Chapter 3  Subprocesses; 1. The definition of Subprocesses. The connexion between subprocesses and multiplicative functionals
Markov processes; theorems and problems by
E. B Dynkin(
Book
)
23 editions published between 1967 and 2014 in 4 languages and held by 487 WorldCat member libraries worldwide
23 editions published between 1967 and 2014 in 4 languages and held by 487 WorldCat member libraries worldwide
Controlled Markov processes by
E. B Dynkin(
Book
)
17 editions published between 1975 and 2013 in 3 languages and held by 446 WorldCat member libraries worldwide
17 editions published between 1975 and 2013 in 3 languages and held by 446 WorldCat member libraries worldwide
Markov processes and related problems of analysis by
E. B Dynkin(
Book
)
37 editions published between 1963 and 2008 in 4 languages and held by 387 WorldCat member libraries worldwide
The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics
37 editions published between 1963 and 2008 in 4 languages and held by 387 WorldCat member libraries worldwide
The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics
Die Grundlagen der Theorie der Markoffschen Prozesse by
E. B Dynkin(
Book
)
24 editions published between 1961 and 2014 in 3 languages and held by 386 WorldCat member libraries worldwide
24 editions published between 1961 and 2014 in 3 languages and held by 386 WorldCat member libraries worldwide
Mathematical conversations by
E. B Dynkin(
Book
)
4 editions published in 1963 in English and held by 348 WorldCat member libraries worldwide
4 editions published in 1963 in English and held by 348 WorldCat member libraries worldwide
Diffusions, superdiffusions, and partial differential equations by
E. B Dynkin(
Book
)
12 editions published in 2002 in English and held by 332 WorldCat member libraries worldwide
12 editions published in 2002 in English and held by 332 WorldCat member libraries worldwide
Mathematical problems; an anthology by
E. B Dynkin(
Book
)
16 editions published between 1967 and 1969 in English and Undetermined and held by 248 WorldCat member libraries worldwide
16 editions published between 1967 and 1969 in English and Undetermined and held by 248 WorldCat member libraries worldwide
Superdiffusions and positive solutions of nonlinear partial differential equations by
E. B Dynkin(
Book
)
9 editions published in 2004 in English and held by 227 WorldCat member libraries worldwide
"This book is devoted to the applications of probability theory to the theory of nonlinear partial differential equations. More precisely, it is shown that all positive solutions for a class of nonlinear elliptic equations in a domain are described in terms of their traces on the boundary of the domain. The main probabilistic tool is the theory of superdiffusions, which describes a random evolution of a cloud of particles. A substantial enhancement of this theory is presented that can be of interest for everybody who works on applications of probabilistic methods to mathematical analysis."Jacket
9 editions published in 2004 in English and held by 227 WorldCat member libraries worldwide
"This book is devoted to the applications of probability theory to the theory of nonlinear partial differential equations. More precisely, it is shown that all positive solutions for a class of nonlinear elliptic equations in a domain are described in terms of their traces on the boundary of the domain. The main probabilistic tool is the theory of superdiffusions, which describes a random evolution of a cloud of particles. A substantial enhancement of this theory is presented that can be of interest for everybody who works on applications of probabilistic methods to mathematical analysis."Jacket
Mathematische Unterhaltungen by
E. B Dynkin(
Book
)
61 editions published between 1955 and 1976 in 4 languages and held by 218 WorldCat member libraries worldwide
61 editions published between 1955 and 1976 in 4 languages and held by 218 WorldCat member libraries worldwide
The Dynkin festschrift : Markov processes and their applications(
Book
)
7 editions published between 1994 and 2013 in English and held by 212 WorldCat member libraries worldwide
Onishchik, A.A. Kirillov, and E.B. Vinberg, who obtained their first results on Lie groups in Dynkin's seminar. At a later stage, the work of the seminar was greatly enriched by the active participation of 1. 1. Pyatetskii Shapiro. As already noted, Dynkin started to work in probability as far back as his undergraduate studies. In fact, his first published paper deals with a problem arising in Markov chain theory. The most significant among his earliest probabilistic results concern sufficient statistics. In [15] and [17], Dynkin described all families of onedimensional probability distributions admitting nontrivial sufficient statistics. These papers have considerably influenced the subsequent research in this field. But Dynkin's most famous results in probability concern the theory of Markov processes. Following Kolmogorov, Feller, Doob and Ito, Dynkin opened a new chapter in the theory of Markov processes. He created the fundamental concept of a Markov process as a family of measures corresponding to var ious initial times and states and he defined time homogeneous processes in terms of the shift operators ()t. In a joint paper with his student A
7 editions published between 1994 and 2013 in English and held by 212 WorldCat member libraries worldwide
Onishchik, A.A. Kirillov, and E.B. Vinberg, who obtained their first results on Lie groups in Dynkin's seminar. At a later stage, the work of the seminar was greatly enriched by the active participation of 1. 1. Pyatetskii Shapiro. As already noted, Dynkin started to work in probability as far back as his undergraduate studies. In fact, his first published paper deals with a problem arising in Markov chain theory. The most significant among his earliest probabilistic results concern sufficient statistics. In [15] and [17], Dynkin described all families of onedimensional probability distributions admitting nontrivial sufficient statistics. These papers have considerably influenced the subsequent research in this field. But Dynkin's most famous results in probability concern the theory of Markov processes. Following Kolmogorov, Feller, Doob and Ito, Dynkin opened a new chapter in the theory of Markov processes. He created the fundamental concept of a Markov process as a family of measures corresponding to var ious initial times and states and he defined time homogeneous processes in terms of the shift operators ()t. In a joint paper with his student A
Lie groups and Lie algebras I by
V. V Gorbatsevich(
Book
)
6 editions published in 1995 in English and held by 196 WorldCat member libraries worldwide
From the reviews: "This volume consists of two parts. ... Part I is devoted to a systematic development of the theory of Lie groups. The Lie algebras are studied only in connection with Lie groups, i.e. a systematic study of the Lie algebras is included here. Neither the structural theory of the Lie groups and Lie algebras nor a systematic study of the topology of Lie groups form the subject of this volume. On the other hand, Part I contains a very interesting chapter on generalizations of Lie groups including very recent results. We find here Lie groups over nonarchimedian fields, formal groups, infinite dimensional Lie groups and also analytic loops. Part II deals on an advanced level with actions of Lie groups on manifolds and includes subjec ts like Lie groups actions on manifolds, transitive actions, actions of compact Lie groups on lowdimensional manifolds. Though the authors state that the geometry and topology of Lie groups is almost entirely beyond the scope of this survey, one can learn a lot in these directions. Both parts are very nicely written and can be strongly recommended." European Mathematical Society Newsletter, 1993 " ... the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source ... This is a hand rather than a textbook. ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" The New Zealand Mathematical Society Newsletter, 1994
6 editions published in 1995 in English and held by 196 WorldCat member libraries worldwide
From the reviews: "This volume consists of two parts. ... Part I is devoted to a systematic development of the theory of Lie groups. The Lie algebras are studied only in connection with Lie groups, i.e. a systematic study of the Lie algebras is included here. Neither the structural theory of the Lie groups and Lie algebras nor a systematic study of the topology of Lie groups form the subject of this volume. On the other hand, Part I contains a very interesting chapter on generalizations of Lie groups including very recent results. We find here Lie groups over nonarchimedian fields, formal groups, infinite dimensional Lie groups and also analytic loops. Part II deals on an advanced level with actions of Lie groups on manifolds and includes subjec ts like Lie groups actions on manifolds, transitive actions, actions of compact Lie groups on lowdimensional manifolds. Though the authors state that the geometry and topology of Lie groups is almost entirely beyond the scope of this survey, one can learn a lot in these directions. Both parts are very nicely written and can be strongly recommended." European Mathematical Society Newsletter, 1993 " ... the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source ... This is a hand rather than a textbook. ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" The New Zealand Mathematical Society Newsletter, 1994
Sätze und Aufgaben über Markoffsche Prozesse by
E. B Dynkin(
Book
)
12 editions published in 1969 in German and Undetermined and held by 189 WorldCat member libraries worldwide
12 editions published in 1969 in German and Undetermined and held by 189 WorldCat member libraries worldwide
Théorie des processus markoviens by
E. B Dynkin(
Book
)
14 editions published between 1962 and 1963 in French and English and held by 166 WorldCat member libraries worldwide
14 editions published between 1962 and 1963 in French and English and held by 166 WorldCat member libraries worldwide
An introduction to branching measurevalued processes by
E. B Dynkin(
Book
)
9 editions published in 1994 in English and held by 156 WorldCat member libraries worldwide
9 editions published in 1994 in English and held by 156 WorldCat member libraries worldwide
Selected papers of E.B. Dynkin with commentary by
E. B Dynkin(
Book
)
8 editions published in 2000 in English and held by 145 WorldCat member libraries worldwide
8 editions published in 2000 in English and held by 145 WorldCat member libraries worldwide
Mathematische Unterhaltungen : Aufgaben über das Mehrfarbenproblem, aus der Zahlentheorie und der Wahrscheinlichkeitsrechnung by
E. B Dynkin(
Book
)
37 editions published between 1955 and 1983 in 3 languages and held by 129 WorldCat member libraries worldwide
37 editions published between 1955 and 1983 in 3 languages and held by 129 WorldCat member libraries worldwide
Markov processes by
E. B Dynkin(
Book
)
13 editions published in 1965 in English and German and held by 80 WorldCat member libraries worldwide
13 editions published in 1965 in English and German and held by 80 WorldCat member libraries worldwide
Mathematical conversations : Multicolor problems, Problems in the theory of numbers, and Random walks by
E. B Dynkin(
Book
)
8 editions published between 2006 and 2013 in English and held by 52 WorldCat member libraries worldwide
Cover; Title Page; Copyright Page; Contents; Section I: Multicolor Problems; Introduction; Chapter 1. Coloring with Two Colors; 1. Simple TwoColor Problems; 2. Problems on Square Boards; 3. Problems Involving Even and Odd Numbers; 4. Networks and Maps; 5. General TwoColor Problems; Chapter 2. Coloring with Three Colors; 6. A simple ThreeColor Problem; 7. Problems on Hexagonal Boards; 8. Dual Diagrams; 9. Triangulation; 10. Dual Maps; 11. Normal Maps in Three Colors; Chapter 3. The FourColor Problem; 12. Normal Maps in Four Colors; 13. Volynskii's Theorem; Chapter 4. The FiveColor Theorem
8 editions published between 2006 and 2013 in English and held by 52 WorldCat member libraries worldwide
Cover; Title Page; Copyright Page; Contents; Section I: Multicolor Problems; Introduction; Chapter 1. Coloring with Two Colors; 1. Simple TwoColor Problems; 2. Problems on Square Boards; 3. Problems Involving Even and Odd Numbers; 4. Networks and Maps; 5. General TwoColor Problems; Chapter 2. Coloring with Three Colors; 6. A simple ThreeColor Problem; 7. Problems on Hexagonal Boards; 8. Dual Diagrams; 9. Triangulation; 10. Dual Maps; 11. Normal Maps in Three Colors; Chapter 3. The FourColor Problem; 12. Normal Maps in Four Colors; 13. Volynskii's Theorem; Chapter 4. The FiveColor Theorem
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Related Identities
 Yushkevich, A. A. (Alexander Adolph) 1930 Editor
 Uspenskiĭ, V. A. (Vladimir Andreevich)
 Freĭdlin, M. I. (Mark Iosifovich) Editor
 Silverman, Richard A. Translator
 Gindikin, S. G. (Semen Grigorʹevich) Other Editor
 Vinberg, Ė. B. (Ėrnest Borisovich) Other Editor
 Sosinskiĭ, A. B. (Alekseĭ Bronislavovich) Translator
 Onishchik, A. L. Editor
 Seitz, Gary M. 1943 Editor
 Uspenskiĭ, Vladimin Aleksandrovich
Useful Links
Associated Subjects
Algebraic topology Branching processes Cell aggregationMathematics Control theory Differential equations, Elliptic Differential equations, Nonlinear Differential equations, Parabolic Differential equations, Partial Diffusion processes Dynkin, E. B.(Evgeniĭ Borisovich), Fourcolor problem Geometry, Algebraic Global differential geometry Lie algebras Lie algebroids Lie groups Linear algebraic groups Markov, A. A.(Andreĭ Andreevich), Markov processes Mathematical optimization Mathematics MathematicsStudy and teaching Probabilities Soviet Union Stochastic analysis Topological groups
Alternative Names
Dynkin, E. B.
Dynkin, E. B. 1924
Dynkin, E.B. 19242014
Dynkin, E. B. (Evgeniĭ Borisovich), 1924
Dynkin, Eug`ne B.
Dynkin, Eugene 19242014
Dynkin, Eugene B.
Dynkin Eugene B. 1924....
Dynkin, Eugene B. 19242014
Dynkin, Eugene Borisovich 19242014
Dynkin, Evgeniĭ B.
Dynkin, Evgeniĭ B. 19242014
Dynkin, Evgenii Borisovič.
Dynkin, Evgeniĭ Borisovich
Dynkin Evgeniĭ Borisovich 1924....
Dynkin, Evgeniĭ Borisovich 19242014
Dynkin, Evgenij Borisovič
Dynkin, Evgenij Borisovič 19242014
Dynkin, Ewgenij Borisowič 1924
Dynkin, J.
Dynkin, Jewgeni B. 19242014
Dynkine Evgueni Borisovitch 1924....
Eugene Dynkin RussianAmerican mathematician
Eugene Dynkin Russisch wiskundige (19242014)
Eugene Dynkin russischer Mathematiker
Eugène Dynkine mathématicien russe
Evgenij Borisovič Dynkin matematico russo
Jevgenij Dinkin
Динкін Євген Борисович
Дынкин, Е. Б.
Дынкин, Е. Б 19242014
Дынкин, Е. Б. (Евгений Борисович), 19242014
Дынкин, Евгений Борисович
Дынкин, Евгений Борисович 19242014
Јевгениј Динкин
예브게니 딘킨
ドゥインキン, イエ・ベ
尤金·登金
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