Kolmogorov Equations for Stochastic PDEs

Beschreibung

Special attention to Kolmogorov equations; it is shown that, in each case, there exists a core of smooth functions. This fact is applied to define Sobolev spaces w.r.t. invariant measures and to prove, e.g., the Poincaré and log-Sobolev inequalities Absolute continuity of the invariant measure w.r.t. a suitable Gaussian measure is studied

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.

Autor*in

Giuseppe Da Prato

Themen in »Kolmogorov Equations for Stochastic PDEs«

Burger's equation Gaussian measure Kolmogorov equations Navier-Stokes Reaction-diffusion equations Sobolev space Stochastic PDE partial differential equation partial differential equations

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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.

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