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" Stochastic equations in infinite dimensions / "
Giuseppe Da Prato, Scuola Normale Superiore, Pisa, Jerzy Zabczyk, Polish Academy of Sciences
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BL
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| Record Number
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640049
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dltt
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| Main Entry
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Da Prato, Giuseppe
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| Title & Author
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Stochastic equations in infinite dimensions /\ Giuseppe Da Prato, Scuola Normale Superiore, Pisa, Jerzy Zabczyk, Polish Academy of Sciences
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| Edition Statement
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Second edition
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| Series Statement
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Encyclopedia of mathematics and its applications ;; 152
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| Page. NO
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xviii, 493 pages ;; 24 cm
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| ISBN
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9781107055841
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: 1107055849
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Includes bibliographical references (pages 446-490) and index
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| Contents
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Introduction: motivating examples -- Part One: Foundations -- Random variables -- Probability measures -- Stochastic processes -- The stochastic integral -- Part Two: Existence and uniqueness -- Linear equations with additive noise -- Linear equations with multiplicative noise -- Existence and uniqueness for nonlinear equations -- Martingale solutions -- Part Three: Properties of solutions -- Markov property and Kolmogorov equation -- Absolute continuity and the Girsanov theorem -- Large time behavior of solutions -- Small noise asymptotic behavior -- Survey of specific equations -- Some recent developments
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| Abstract
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"Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional spaces, typically Hilbert and Banach spaces. In the first part the authors give an exposition of the main properties of probability measures on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions.Appendices gather together background results from analysis that are otherwise hard to find under one roof. This revised edition includes two brand new chapters surveying recent developments in the field and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations"--
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Stochastic partial differential equations
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Zabczyk, Jerzy
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