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.
%0 Journal Article
%1 20db2c27fa7b445e8b652bf2e17af642
%A Oechsler, David
%D 2023
%I Springer, Dordrecht u. a.
%J Statistics and Computing
%K Carlo, FIS_scads Invariant Langevin Limiting L{\'e}vy Monte Stochastic differential distributions, equations processes, yaff
%N 1
%R 10.1007/s11222-023-10345-w
%T Lévy Langevin Monte Carlo
%V 34 (2024)
%X 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.
@article{20db2c27fa7b445e8b652bf2e17af642,
abstract = {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 L{\'e}vy 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.},
added-at = {2024-11-28T16:27:18.000+0100},
author = {Oechsler, David},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/299e0fb706154b5bd080597286166e05b/scadsfct},
day = 10,
doi = {10.1007/s11222-023-10345-w},
interhash = {211406f48877e40877da47fb6f1e9d60},
intrahash = {99e0fb706154b5bd080597286166e05b},
issn = {0960-3174},
journal = {Statistics and Computing},
keywords = {Carlo, FIS_scads Invariant Langevin Limiting L{\'e}vy Monte Stochastic differential distributions, equations processes, yaff},
language = {English},
month = nov,
note = {Publisher Copyright: {\textcopyright} 2023, The Author(s).},
number = 1,
publisher = {Springer, Dordrecht [u. a.]},
timestamp = {2025-07-29T10:29:43.000+0200},
title = {L{\'e}vy Langevin Monte Carlo},
volume = {34 (2024)},
year = 2023
}
