Stochastic equations in infinite dimensions

• 作者： Da Prato, Giuseppe, author.
• 其他作者：
  • Zabczyk, Jerzy, author.
• 其他題名：
  • Encyclopedia of mathematics and its applications ;
• 出版： Cambridge : Cambridge University Press
• 版本：Second edition.
• 叢書名： Encyclopedia of mathematics and its applications ;152
• 主題： Stochastic partial differential equations.
• ISBN： 9781107295513 (electronic bk.) 、 9781107055841 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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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• 摘要註: Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part the authors give a self-contained exposition of the basic properties of probability measure 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 area 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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