Recent advances in various fields of numerical probability^*,**

¹ Université Paris-Est, CERMICS (ENPC), 6-8-10 Avenue Blaise Pascal, Cité Descartes, F-77455 Marne-la-Vallée, France ;
brehierc@cermics.enpc.fr
² INRIA Paris-Rocquencourt, Domaine de Voluceau - Rocquencourt, B.P. 105 - 78153 Le Chesnay, France ;
charles-edouard.brehier@inria.fr
³ IUT de Chambery, LAMA, UMR 5127,Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France,
E-mail: pe.deraynal@univ-savoie.fr
⁴ Laboratoire de Probabilités et Modèles Aléatoires, UMR 7599, UPMC, Case 188, 4 pl. Jussieu, F-75252 Paris Cedex 5, France,
E-mail: vincent.lemaire@upmc.fr
⁵ Institut de Mathématiques de Toulouse, Université Paul Sabatier&INSA Toulouse, 135, av. de Rangueil, F-31077 Toulouse Cedex 4, France,
E-mail: fabien.panloup@math.univ-toulouse.fr
⁶ CERMICS-École des Ponts Paris Tech, 6 et 8 avenue Blaise Pascal, Cité Descartes - Champs sur Marne, 77455 Marne la Vallée Cedex 2, France,
E-mail: reyc@cermics.enpc.fr

Abstract

The goal of this paper is to present a series of recent contributions on some various problems of numerical probability. Beginning with the Richardson-Romberg Multilevel Monte-Carlo method which, among other fields of applications, is a very efficient method for the approximation of diffusion processes, we focus on some adaptive multilevel splitting algorithms for rare event simulation. Then, the third part is devoted to the simulation of McKean-Vlasov forward and decoupled forward-backward stochastic differential equations by some cubature algorithms. Finally, we tackle the problem of the weak error estimation in total variation norm for a general Markov semi-group.