Simulation and numerical analysis of stochastic differential systems : a review
Résumé
We present methods of approximating quantities related to the solutions of stochastic differential systems based on the simulation of time-discrete Markov chains. The motivations come from random mechanics and the numerical integration of certains deterministic P.D.E.'s by probabilistic algorithms. We state theoretical results concerning the rates of convergence of these methods. We give results of numerical tests, and we describe an application of this approach to an engineering problem (the study of stability of the motion of a helicopter blade).