Stochastic Cauchy Problems in Infinite Dimensions

Generalized and Regularized Solutions

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Differential Equations
Cover of the book Stochastic Cauchy Problems in Infinite Dimensions by Irina V. Melnikova, CRC Press
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Author: Irina V. Melnikova ISBN: 9781315360263
Publisher: CRC Press Publication: September 3, 2018
Imprint: Chapman and Hall/CRC Language: English
Author: Irina V. Melnikova
ISBN: 9781315360263
Publisher: CRC Press
Publication: September 3, 2018
Imprint: Chapman and Hall/CRC
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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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