Concentration inequalities for Euler schemes

Florent Malrieu (1) , Denis Talay (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 TOSCA - Simuler et calibrer des modèles stochastiques

We establish a Poincare inequality for the law at time t of the explicit Euler scheme for a stochastic differential equation. When the diffusion coefficient is constant, we also establish a Logarithmic Sobolev inequality for both the explicit and implicit Euler scheme, with a constant related to the convexity of the drift coefficient. Then we provide exact confidence intervals for the convergence of Monte Carlo methods.

Domaines: Probabilités [math.PR]

Florent Malrieu, Denis Talay. Concentration inequalities for Euler schemes. Niederreiter, Harald and Talay, Denis. Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, pp.355-371, 2006. ⟨hal-00452108⟩