Diffusions, Superdiffusions and Partial Differential Equations

E. B. Dynkin

Published by American Mathematical Society, 2002
ISBN 10: 0821831747 / ISBN 13: 9780821831748
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Brand new. We distribute directly for the publisher. 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. Bookseller Inventory #

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Synopsis: 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.

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Title: Diffusions, Superdiffusions and Partial ...
Publisher: American Mathematical Society
Publication Date: 2002
Binding: Hardcover
Book Condition: New

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Book Description American Mathematical Society, United States, 2002. Hardback. Condition: New. Language: English . Brand New Book. 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. Seller Inventory # AAN9780821831748

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Book Description American Mathematical Society, United States, 2002. Hardback. Condition: New. Language: English . Brand New Book. 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. Seller Inventory # AAN9780821831748

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