Lévy-Langevin Monte Carlo
A talk in the Oberseminar Probability Theory and Mathematical Statistics series by
Anita Behme from TU Dresden
| Abstract: | We present a distributional equation for invariant measures of Markov processes that are associated to Lévy-type operators. Particular focus is put on the one-dimensional case where the distributional equation becomes a Volterra-Fredholm integral equation, and on solutions to Lévy-driven stochastic differential equations.
The latter case is then used to develop a method to sample from a target distribution by simulating a solution of a stochastic differential equation. The approach is similar to the well-known Langevin Monte Carlo method based on stochastic differential equations driven by Brownian motion. However, using a general Lévy process as noise term yields an algorithm suitable to sample from non-smooth, multimodal or even heavy-tailed targets that are unreachable by classic approaches. This talk is based on joint works with David Oechsler and Claudius Lütke Schwienhorst. |