Kolmogorov Equations for Stochastic PDEs (Advanced Courses in Mathematics - CRM Barcelona)
Edition: 1 edition
Publisher: Birkhäuser Basel
Published: February 14, 2005
Language: eng
Format: Paperback
Number of pages: 182
ISBN-13: 9783764372163
Subjects: Probability & statistics; Mathematics; Science/Mathematics; Computer Science; Differential Equations - Partial Differential Equations; Probability & Statistics - General; Burger's equation; Mathematics / Differential Equations; Navier-Stokes; Reaction-diffusion equations; Stochastic PDE; Differential Equations
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.