Analogously to the well-known Langevin Monte Carlo method, in this article we provide a method to sample from a target distribution π by simulating a solution of a stochastic differential equation. Hereby, the stochastic differential equation is driven by a general Lévy process which—unlike 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 , ∞) and a compound Poisson driving noise. Several illustrative examples conclude the article.