Kolmogorov Equations for Stochastic PDEs (Advanced Courses in Mathematics - CRM Barcelona)
1 edition
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Word Count
45,500 words, Guess
Page Count
182 pages
Physical Format
Paperback
Identifiers
- Open LibraryOL9090952M
- ISBN-139783764372163
- ISBN-103764372168
- OCLC Control Number56967057
- Library of Congress Control Number2004062668
and 2 more
- Goodreads1043472
- LibraryThing4992640
Classifications
- LCCQA377 .D3 2004
Description
The subject of this book is stochastic partial differential equations, in particular, reaction-diffusion equations, Burgers and Navier-Stokes equations and the corresponding Kolmogorov equations. For each case the transition semigroup is considered and irreducibility, the strong Feller property, and invariant measures are investigated. Moreover, it is proved that the exponential functions provide a core for the infinitesimal generator. As a consequence, it is possible to study Sobolev spaces with respect to invariant measures and to prove a basic formula of integration by parts (the so-called "carré du champs identity". Several results were proved by the author and his collaborators and appear in book form for the first time. Presenting the basic elements of the theory in a simple and compact way, the book covers a one-year course directed to graduate students in mathematics or physics. The only prerequisites are basic probability (including finite dimensional stochastic differential equations), basic functional analysis and some elements of the theory of partial differential equations.
Subjects
Topics
Other Editions
- Kolmogorov Equations for Stochastic PDEs (Advanced Courses in Mathematics - CRM Barcelona)
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