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Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions

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by Irina V. Melnikova
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Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions by Irina V. Melnikova

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.

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Ebook Details
Pages: 286
Size: 3.3 MB
Publisher: Chapman and Hall/CRC
Date published:   2016
ISBN: 9781498785853 (DRM-EPUB)
9781482210514 (DRM-PDF)

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This product is listed in the following categories:

Nonfiction > Mathematics
Nonfiction > Mathematics > Differential Equations
Nonfiction > Mathematics > Functional Analysis

This author has products in the following categories:

Nonfiction > Mathematics
Nonfiction > Mathematics > Differential Equations
Nonfiction > Mathematics > Functional Analysis
Nonfiction > Science > Mathematical Physics

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03/30/2017
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