Concentration Inequalities for Euler Schemes

Florent Malrieu () and Denis Talay ()
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Florent Malrieu: IRMAR
Denis Talay: INRIA Sophia-Antipolis

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 355-371 from Springer

Abstract: Summary We establish a Poincaré 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.

Keywords: Commutation Relation; Particle System; Euler Scheme; Transition Kernel; Logarithmic Sobolev Inequality (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-31186-7_21

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DOI: 10.1007/3-540-31186-6_21

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