Geodesic
Numerical methods for Stochastic differential equations: two examples
Paul-Éric Chaudru de Raynal1 ; Gilles Pagès2 ; Clément Rey3
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
ESAIM. Proceedings, Tome 64 (2018), pp. 65-77.

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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.
DOI : 10.1051/proc/201864065

Paul-Éric Chaudru de Raynal 1 ; Gilles Pagès 2 ; Clément Rey 3

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 
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     title = {Numerical methods for {Stochastic} differential equations: two examples},
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Paul-Éric Chaudru de Raynal; Gilles Pagès; Clément Rey. Numerical methods for Stochastic differential equations: two examples. ESAIM. Proceedings, Tome 64 (2018), pp. 65-77. doi : 10.1051/proc/201864065. http://geodesic.mathdoc.fr/articles/10.1051/proc/201864065/

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