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Lévy Langevin Monte Carlo
David Oechsler · 2023-03-14 · via math.PR updates on arXiv.org

Analogue 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 - 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.

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