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.
CITATION STYLE
Malrieu, F., & Talay, D. (2006). Concentration Inequalities for Euler Schemes. In Monte Carlo and Quasi-Monte Carlo Methods 2004 (pp. 355–371). Springer-Verlag. https://doi.org/10.1007/3-540-31186-6_21
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