L\'evy Langevin Monte Carlo

Analogue to the well-known Langevin Monte Carlo method, in this article we provide a method to sample from a target distribution $\pi$ by simulating a solution of a stochastic differential equation. Hereby, the stochastic differential equation is driven by a general L\'evy process which - other than in the case of Langevin Monte Carlo - allows for non-smooth targets. Our method will be fully explored in the particular setting of target distributions supported on the half-line $(0,\infty)$ and a compound Poisson driving noise. Several illustrative examples conclude the article.