This textbook gives an introduction to shastic 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 shastic differential equations), basic functional analysis and some elements of the theory of partial differential equations.
This textbook gives an introduction to shastic 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 shastic differential equations), basic functional analysis and some elements of the theory of partial differential equations.
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