Concentration inequalities for Euler schemes

Florent Malrieu 1 Denis Talay 2
2 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : 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.
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Submitted on : Monday, February 1, 2010 - 3:30:50 PM
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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〉

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