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Stochastic Differential Equations in Infinite Dimensions: with Applications to Stochastic Partial Differential Equations
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Catalogue Information
Field name
Details
Dewey Class
519.22
Title
Stochastic Differential Equations in Infinite Dimensions ([Ebook]) : with Applications to Stochastic Partial Differential Equations / by Leszek Gawarecki, Vidyadhar Mandrekar.
Author
Gawarecki, Leszek
Added Personal Name
Mandrekar, Vidyadhar
Other name(s)
SpringerLink (Online service)
Publication
Berlin, Heidelberg : Springer , 2011.
Physical Details
XVI, 292 pages : online resource.
Series
Probability and Its Applications
1431-7028
ISBN
9783642161940
Summary Note
The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE's. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.:
Contents note
Preface -- Part I: Stochastic Differential Equations in Infinite Dimensions -- 1.Partial Differential Equations as Equations in Infinite -- 2.Stochastic Calculus -- 3.Stochastic Differential Equations -- 4.Solutions by Variational Method -- 5.Stochastic Differential Equations with Discontinuous Drift -- Part II: Stability, Boundedness, and Invariant Measures -- 6.Stability Theory for Strong and Mild Solutions -- 7.Ultimate Boundedness and Invariant Measure -- References -- Index.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-3-642-16194-0
Links to Related Works
Subject References:
Applications of Mathematics
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Differential equations, Partial
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Distribution (Probability theory)
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Finance
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Partial differential equations
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Probability theory and stochastic processes
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Quantitative Finance
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Stochastic differential equations
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Authors:
author
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Gawarecki, Leszek
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Mandrekar, Vidyadhar
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Corporate Authors:
SpringerLink (Online service)
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Series:
Probability and Its Applications
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Classification:
519.22
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519.22 (DDC 23)
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