Markov Processes: Theorems and Problems

Science & Math

E. B. Dynkin

Mathematics

Springer

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.

Selected Papers of E. B. Dynkin with Commentary

American Mathematical Society

Eleven Papers on Analysis, Probability and Topology (American Mathematical Society Translations--series 2)

I. M. Gel'fand

M.A. Krasnosel'skii

A. O Gelfond

A.Ja. Hincin

Amer Mathematical Society

<p>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.</p>

Diffusions, Superdiffusions and Partial Differential Equations

Markov Processes (Grundlehren der mathematischen Wissenschaften, Vol. 121) (2 Volumes)

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Books by E. B. Dynkin