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Stochastic equations in infinite dim...

Da Prato, Giuseppe.

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Stochastic equations in infinite dimensions

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Stochastic equations in infinite dimensions/ Giuseppe Da Prato, Jerzy Zabczyk.
作者:	Da Prato, Giuseppe.
其他作者:	Zabczyk, Jerzy.
出版者:	Cambridge :Cambridge University Press, : 2014.,
面頁冊數:	xviii, 493 p. :ill., digital ;24 cm.
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.
標題:	Stochastic partial differential equations. -
電子資源:	https://doi.org/10.1017/CBO9781107295513
ISBN:	9781107295513

Stochastic equations in infinite dimensions
Da Prato, Giuseppe.

Stochastic equations in infinite dimensions[electronic resource] /Giuseppe Da Prato, Jerzy Zabczyk. - 2nd ed. - Cambridge :Cambridge University Press,2014. - xviii, 493 p. :ill., digital ;24 cm. - Encyclopedia of mathematics and its applications ;152. - Encyclopedia of mathematics and its applications ;152..

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.

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.

ISBN: 9781107295513Subjects--Topical Terms:

625093
Stochastic partial differential equations.

LC Class. No.: QA274.25 / .D4 2014

Dewey Class. No.: 519.22

Stochastic equations in infinite dimensions
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490 1 $a Encyclopedia of mathematics and its applications ; $v 152
505 0 $a 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.
520 $a 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.
650 0 $a Stochastic partial differential equations. $3 625093
700 1 $a Zabczyk, Jerzy. $3 625091
830 0 $a Encyclopedia of mathematics and its applications ; $v 152. $3 3400123
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