Kolmogorov Equations for Stochastic PDEs (Advanced Courses in Mathematics - CRM Barcelona) - Softcover

Da Prato, Giuseppe

Softcover

ISBN 10: 3764372168 ISBN 13: 9783764372163

Publisher: Birkhäuser, 2004

Synopsis

This textbook gives an introduction to stochastic partial differential equations such as reaction-diffusion, Burgers and 2D Navier-Stokes equations, perturbed by noise. Several properties of corresponding transition semigroups are studied, such as Feller and strong Feller properties, irreducibility, existence and uniqueness of invariantg measures. Moreover, the transition semigroups are interpreted as generalized solutions of Kologorov equations.
The prerequisites are basic probability (including finite dimemsional stochastic differential equations), basic functional analysis and some elements of the theory of partial differential equations.

About this title

Review

Many of the results presented here are appearing in book form for the first time. (...) The writing style is clear. Needless to say, the level of mathematics is high and will no doubt tax the average mathematics and physics graduate student. For the devoted student, however, this book offers an excellent basis for a 1-year course on the subject. It is definitely recommended.

JASA Reviews

Synopsis

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 "carre 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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2004
• ISBN 10: 3764372168
• ISBN 13: 9783764372163
• Binding: Paperback
• Language: English
• Number of pages: 189