Cooling down stochastic differential equations: almost sure convergence

S. Dereich, S. Kassing

We consider almost sure convergence of the SDE $d{X}_t={\alpha }_{t}dt+{\beta }_{t}d{W}_t$ under the existence of a $C^2$-Lyapunov function $F:{\mathbb{R}}^d\to \mathbb{R}$. More explicitly, we show t…