Background
Dynkin, Eugene B. was born on May 11, 1924 in Leningrad, Union of the Soviet Socialist Republics. Came to the United States, 1977, naturalized, 1983. Son of Boris and Rebecca (Sheindlin) Dynkin.
(The theory of Markov Processes has become a powerful tool...)
The theory of Markov Processes has become a powerful tool in partial differential equations and potential theory with important applications to physics. Professor Dynkin has made many profound contributions to the subject and in this volume are collected several of his most important expository and survey articles. The content of these articles has not been covered in any monograph as yet. This account is accessible to graduate students in mathematics and operations research and will be welcomed by all those interested in stochastic processes and their applications.
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(For about half a century, two classes of stochastic proce...)
For about half a century, two classes of stochastic processes--Gaussian processes and processes with independent increments--have played an important role in the development of stochastic analysis and its applications. During the last decade, a third class--branching measure-valued (BMV) processes--has also been the subject of much research. A common feature of all three classes is that their finite-dimensional distributions are infinitely divisible, allowing the use of the powerful analytic tool of Laplace (or Fourier) transforms. All three classes, in an infinite-dimensional setting, provide means for study of physical systems with infinitely many degrees of freedom. This is the first monograph devoted to the theory of BMV processes. Dynkin first constructs a large class of BMV processes, called superprocesses, by passing to the limit from branching particle systems. Then he proves that, under certain restrictions, a general BMV process is a superprocess. A special chapter is devoted to the connections between superprocesses and a class of nonlinear partial differential equations recently discovered by Dynkin.
http://www.amazon.com/gp/product/0821802690/?tag=2022091-20
(Translated from the Russian by Norman D. Whaland, Jr., an...)
Translated from the Russian by Norman D. Whaland, Jr., and Robert B. Brown, as part of the Survey of Recent East European Mathematical Literature, under Alfred L. Putnam and Izaak Wirszup. Originally published in Russian in 1952, as part of the Library of the Mathematics Circle.
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(This book is devoted to the systematic exposition of the ...)
This book is devoted to the systematic exposition of the contemporary theory of controlled Markov processes with discrete time parameter or in another termi nology multistage Markovian decision processes. We discuss the applications of this theory to various concrete problems. Particular attention is paid to mathe matical models of economic planning, taking account of stochastic factors. The authors strove to construct the exposition in such a way that a reader interested in the applications can get through the book with a minimal mathe matical apparatus. On the other hand, a mathematician will find, in the appropriate chapters, a rigorous theory of general control models, based on advanced measure theory, analytic set theory, measurable selection theorems, and so forth. We have abstained from the manner of presentation of many mathematical monographs, in which one presents immediately the most general situation and only then discusses simpler special cases and examples. Wishing to separate out difficulties, we introduce new concepts and ideas in the simplest setting, where they already begin to work. Thus, before considering control problems on an infinite time interval, we investigate in detail the case of the finite interval. Here we first study in detail models with finite state and action spaces-a case not requiring a departure from the realm of elementary mathematics, and at the same time illustrating the most important principles of the theory.
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( An investigation of the logical foundations of the theo...)
An investigation of the logical foundations of the theory behind Markov random processes, this text explores subprocesses, transition functions, and conditions for boundedness and continuity. Rather than focusing on probability measures individually, the work explores connections between functions. An elementary grasp of the theory of Markov processes is assumed. Starting with a brief survey of relevant concepts and theorems from measure theory, the text investigates operations that permit an inspection of the class of Markov processes corresponding to a given transition function. It advances to the more complicated operations of generating a subprocess, followed by examinations of the construction of Markov processes with given transition functions, the concept of a strictly "Markov process," and the conditions required for boundedness and continuity of a Markov process. Addenda, notes, references, and indexes supplement the text.
http://www.amazon.com/gp/product/0486453057/?tag=2022091-20
(This book is devoted to the systematic exposition of the ...)
This book is devoted to the systematic exposition of the contemporary theory of controlled Markov processes with discrete time parameter or in another termi nology multistage Markovian decision processes. We discuss the applications of this theory to various concrete problems. Particular attention is paid to mathe matical models of economic planning, taking account of stochastic factors. The authors strove to construct the exposition in such a way that a reader interested in the applications can get through the book with a minimal mathe matical apparatus. On the other hand, a mathematician will find, in the appropriate chapters, a rigorous theory of general control models, based on advanced measure theory, analytic set theory, measurable selection theorems, and so forth. We have abstained from the manner of presentation of many mathematical monographs, in which one presents immediately the most general situation and only then discusses simpler special cases and examples. Wishing to separate out difficulties, we introduce new concepts and ideas in the simplest setting, where they already begin to work. Thus, before considering control problems on an infinite time interval, we investigate in detail the case of the finite interval. Here we first study in detail models with finite state and action spaces-a case not requiring a departure from the realm of elementary mathematics, and at the same time illustrating the most important principles of the theory.
http://www.amazon.com/gp/product/0387903879/?tag=2022091-20
(Interactions between the theory of partial differential e...)
Interactions between the theory of partial differential equations of elliptic and parabolic types and the theory of stochastic processes are beneficial for both probability theory and analysis. At the beginning, mostly analytic results were used by probabilists. More recently, analysts (and physicists) took inspiration from the probabilistic approach. Of course, the development of analysis in general and of the theory of partial differential equations in particular, was motivated to a great extent by problems in physics. A difference between physics and probability is that the latter provides not only an intuition, but also rigorous mathematical tools for proving theorems. The subject of this book is connections between linear and semilinear differential equations and the corresponding Markov processes called diffusions and superdiffusions. Most of the book is devoted to a systematic presentation (in a more general setting, with simplified proofs) of the results obtained since 1988 in a series of papers of Dynkin and Dynkin and Kuznetsov. Many results obtained originally by using superdiffusions are extended in the book to more general equations by applying a combination of diffusions with purely analytic methods. Almost all chapters involve a mixture of probability and analysis. Similar to the other books by Dynkin, Markov Processes (Springer-Verlag), Controlled Markov Processes (Springer-Verlag), and An Introduction to Branching Measure-Valued Processes (American Mathematical Society), this book can become a classical account of the presented topics.
http://www.amazon.com/gp/product/0821831747/?tag=2022091-20
(Eugene Dynkin is a rare example of a contemporary mathema...)
Eugene Dynkin is a rare example of a contemporary mathematician who has achieved outstanding results in two quite different areas of research: algebra and probability. In both areas, his ideas constitute an essential part of modern mathematical knowledge and form a basis for further development. Although his last work in algebra was published in 1955, his contributions continue to influence current research in algebra and in the physics of elementary particles. His work in probability is part of both the historical and the modern development of the topic. This volume presents Dynkin's scientific contributions in both areas. Included are Commentary by recognized experts in the corresponding fields who describe the time, place, role, and impact of Dynkin's research and achievements. Biographical notes and the recollections of his students are also featured.
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( Combining three books into a single volume, this text c...)
Combining three books into a single volume, this text comprises Multicolor Problems, dealing with several of the classical map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; and Random Walks, addressing basic problems in probability theory. The book's primary aim is not so much to impart new information as to teach an active, creative attitude toward mathematics. The sole prerequisites are high-school algebra and (for Multicolor Problems) a familiarity with the methods of mathematical induction. The book is designed for the reader's active participation. The problems are carefully integrated into the text and should be solved in order. Although they are basic, they are by no means elementary. Some sequences of problems are geared toward the mastery of a new method, rather than a definitive result, and others are practice exercises, designed to introduce new concepts. Complete solutions appear at the end.
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Dynkin, Eugene B. was born on May 11, 1924 in Leningrad, Union of the Soviet Socialist Republics. Came to the United States, 1977, naturalized, 1983. Son of Boris and Rebecca (Sheindlin) Dynkin.
Bachelor, Moscow University, 1945. Doctor of Philosophy, Moscow University, 1948. Doctor of Science, Moscow University, 1951.
Doctor Honoris Causa, University Pierre and Marie Curie, Paris, 1997. Doctor Honoris Causa, Indiana Moscow University. Doctor Honoris Causa, University Warwick, United Kingdom, 2003.
Assistant professor, Moscow U., 1948-1949; associate professor, Moscow U., 1949-1954; professor, Moscow U., 1954-1968; senior research scholar, Central Institute Mathematics Economics Academy of Science, Moscow, 1968-1976; professor mathematics, Cornell Univercity, Ithaca, New York, since 1977.
( Combining three books into a single volume, this text c...)
(For about half a century, two classes of stochastic proce...)
(This book is devoted to the systematic exposition of the ...)
(This book is devoted to the systematic exposition of the ...)
(Interactions between the theory of partial differential e...)
( An investigation of the logical foundations of the theo...)
(Eugene Dynkin is a rare example of a contemporary mathema...)
(The theory of Markov Processes has become a powerful tool...)
(Translated from the Russian by Norman D. Whaland, Jr., an...)
(book)
Fellow: American Association for the Advancement of Science, Institute of Mathematics Statistics. Member: National Academy of Sciences, Bernoulli Society Mathematics Statistics and Probability, Moscow Mathematics Society (honorary prize 1951), American Mathematics Society (Leroy P. Steele prize 1993).
Married Irene Pakshver, June 2, 1959. 1 child, Olga.