Stochastic Cauchy problems in infinite dimensions : generalized and regularized solutions
Author(s)
Bibliographic Information
Stochastic Cauchy problems in infinite dimensions : generalized and regularized solutions
（Monographs and research notes in mathematics）
CRC Press, c2016
- : hbk
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Note
Includes bibliographical references (p. 275-282) and index
Description and Table of Contents
Description
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory.
The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.
Table of Contents
Well-Posed and Ill-Posed Abstract Cauchy Problems. The Concept of Regularization: Semi-group methods for construction of exact, approximated, and regularized solutions. Distribution methods for construction of generalized solutions to ill-posed Cauchy problems. Examples. Supplements. Infinite-Dimensional Stochastic Cauchy Problems: Weak, regularized, and mild solutions to Ito integrated stochastic Cauchy problems in Hilbert spaces. Infinite-dimensional stochastic Cauchy problems with white noise processes in spaces of distributions. Infinite-dimensional extension of white noise calculus with application to stochastic problems.
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