Volume 64, 2018SMAI 2017 - 8e Biennale Française des Mathématiques Appliquées et Industrielles
|Page(s)||65 - 77|
|Published online||20 November 2018|
Numerical methods for Stochastic differential equations: two examples
LAMA, Université Savoie Mont Blanc, firstname.lastname@example.org
2 LPSM, UPMC, email@example.com
3 LPSM, UPMC, firstname.lastname@example.org
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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