Kolmogorov Equations

8 January 2009 - 10 January 2009

Aims

Kolmogorov equations are deterministic partial differential equations, motivated by, and strongly connected, to stochastic evolution equations. The general theory (finite dimensional) of stochastic ordinary differential equations is classical and well developed, while the (infinite dimensional) theory of stochastic partial differential equations is still largely open. Therefore, a large part of the workshop is devoted to stochastic evolution equations in infinite-dimensional Hilbert spaces, with particularattention to mathematical models of interest, such as the Burgers equation, reaction-diffusion systems, Navier-Stokes equations, Volterra equations, perturbed by noise.

Besides existence and uniqueness of the solutions to finite and infinite dimensional Kolmogorov equations, the current research deals with regularity properties both of analytic and of stochastic type, existence and uniqueness of invariant measures and asymptotic properties of the associated transition semigroups like ergodicity.

The heart of the workshop is the interaction between deterministic and stochastic methods, which is natural because of the strong connection between stochastic differential equations and the associated Kolmogorov equations, and that give complementary results.