Issue |
ESAIM: ProcS
Volume 64, 2018
SMAI 2017 - 8e Biennale Française des Mathématiques Appliquées et Industrielles
|
|
---|---|---|
Page(s) | 65 - 77 | |
DOI | https://doi.org/10.1051/proc/201864065 | |
Published online | 20 November 2018 |
Numerical methods for Stochastic differential equations: two examples
1
LAMA, Université Savoie Mont Blanc, pe.deraynal@univ-savoie.fr
2
LPSM, UPMC, gilles.pages@upmc.fr
3
LPSM, UPMC, clement.rey@upmc.fr
The goal of this paper is to present a series of recent contributions arising in numerical probability. First we present a contribution to a recently introduced problem: stochastic differential equations with constraints in law, investigated through various theoretical and numerical viewpoints. Such a problem may appear as an extension of the famous Skorokhod problem. Then a generic method to approximate in a weak way the invariant distribution of an ergodic Feller process by a Langevin Monte Carlo simulation. It is an extension of a method originally developed for diffusions and based on the weighted empirical measure of an Euler scheme with decreasing step. Finally, we mention without details a recent development of a multilevel Langevin Monte Carlo simulation method for this type of problem.
© EDP Sciences, SMAI 2018
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