Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions - Chapman & Hall/CRC Monographs and Research Notes in Mathematics (Hardback)Irina V. Melnikova (author)
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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.
Publisher: Apple Academic Press Inc.
Number of pages: 286
Weight: 544 g
Dimensions: 235 x 156 mm
"Written by a distinguished expert in the field of generalized functions and semigroups of operators, the book represents an excellent introduction to a theory of increasing power and relevance in contemporary stochastic analysis. [...] Due to its clear, systematic and comprehensive style of exposition, it will make the subject accessible to a broad mathematical audience. [...] The book is designed to be most appealing for graduate students, postgraduates and experienced scientists who work in the field of stochastic partial differential equations, but it should be welcome in the library of any researcher who has a broad mathematical interest."
- Dora Selesi, Mathematical Reviews, March 2017