Stochastic Cauchy Problems in Infinite Dimensions

Released on by Irina V. Melnikova
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  • Stochastic Cauchy Problems in Infinite Dimensions Book Detail

  • Author : Irina V. Melnikova
  • Release Date : 2018-09-03
  • Publisher : CRC Press
  • Genre : Mathematics
  • Pages : 281
  • ISBN 13 : 1315360268
  • File Size : 19,19 MB
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Stochastic Cauchy Problems in Infinite Dimensions by Irina V. Melnikova PDF Summary

Book 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.

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Diagram Genus, Generators, and Applications

Diagram Genus, Generators, and Applications

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In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). Diagram Genus, Generators and Appli