Synopses & Reviews
Kolmogorov Equations for Stochastic PDEs gives an introduction to stochastic partial differential equations, such as reaction-diffusion, Burgers and 2D Navier-Stokes equations, perturbed by noise. It studies several properties of corresponding transition semigroups, such as Feller and strong Feller properties, irreducibility, existence and uniqueness of invariant measures. In addition, the transition semigroups are interpreted as generalized solutions of Kologorov equations.
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
Table of Contents
Introduction and Preliminaries.- Stochastic Perturbations of Linear Equations.- Stochastic Differential Equations with Lipschitz Nonlinearities.- Reaction-Diffusion Equations.- The Stochastic Burgers Equation.- The Stochastic 2D Navier-Stokes Equation.- Bibliography.- Index.