Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes

Exponential Ergodicity for Stochastic Burgers and 2d Navier-stokes Equations

It is shown that transition measures of the stochastic Navier-Stokes equation in 2D converge exponentially fast to the corresponding invariant measures in the distance of total variation. As a corollary we obtain the existence of spectral gap for a related semigroup obtained by a sort of ground state trasformation. Analogous results are proved for the stochastic Burgers equation.

Existence and Ergodicity for the Two-dimensional Stochastic Boussinesq Equation

The existence of solutions to the Boussinesq system driven by random exterior forcing terms both in the velocity field and the temperature is proven using a semigroup approach. We also obtain the existence and uniqueness of an invariant measure via coupling methods.

Exponential Ergodicity of killed Lévy processes in a finite interval

Following Bertoin who considered the ergodicity and exponential decay of Lévy processes in a finite domain [4], we consider general Lévy processes and their ergodicity and exponential decay in a finite interval. More precisely, given Ta = inf{t > 0 : Xt / ∈ (0, a)}, a > 0 and X a Lévy process then we study from spectral-theoretical point of view the killed process P (Xt ∈ ., Ta > t). Under gene...

Exponential Ergodicity of Non-lipschitz Stochastic Differential Equations

Using the coupling method and Girsanov’s theorem, we study the strong Feller property and irreducibility for the transition probabilities of stochastic differential equations with non-Lipschitz and monotone coefficients. Then, the exponential ergodicity and the spectral gap for the corresponding transition semigroups are obtained under fewer assumptions.

Diffusion Equation and Stochastic Processes.