Abstract
We investigate a weighted multilevel Richardson–Romberg extrapolation for the ergodic approximation of invariant distributions of diffusions adapted from the one introduced in [Bernoulli 23 (2017) 2643–2692] for regular Monte Carlo simulation. In a first result, we prove under weak confluence assumptions on the diffusion, that for any integer
Finally, we numerically test this multilevel Langevin estimator on several examples including the simple one-dimensional Ornstein–Uhlenbeck process but also a high dimensional diffusion motivated by a statistical problem. These examples confirm the theoretical efficiency of the method.
Citation
Gilles Pagès. Fabien Panloup. "Weighted multilevel Langevin simulation of invariant measures." Ann. Appl. Probab. 28 (6) 3358 - 3417, December 2018. https://doi.org/10.1214/17-AAP1364
Information