Stochastic Cauchy Problems in Infinite Dimensions

Irina V. Melnikova is a professor in the Institute of Mathematics and Computer Sciences at Ural Federal University. Her research interests include analysis, applied mathematics, and probability theory.

• 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 Itô 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.

"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 Seleši, Mathematical Reviews, March 2017