Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics

# Friday, October 13, 2017 - 14:15 in D5-153

## Ergodicity of stochastic differential equations with distribution drifts.

A talk in the 'Topics Seminar Analysis' series by
Guohuan Zhao from CAS Beijing
 Abstract: We consider the SDE $dX_t=\sigma(X_t)d W_t+b(X_t)dt$ in d-dimensional Euclidean space. We formulate the notion of solution and prove weak existence and uniqueness result when $\sigma$ is in $\dot{H}^{1/2,p}$ and $b$ is only a distribution in $H^{-1/2, p}_loc$. I will also show that the ergodic property holds if $b$ can be written as $b=b_1+b_2$, where $b_1$ is continuous and satisfying the usual dissipative type conditions and $b_2$ is in $H^{-1/2, p}$.