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.
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Malrieu, F., Talay, D. (2006). Concentration Inequalities for Euler Schemes. In: Niederreiter, H., Talay, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31186-6_21
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DOI: https://doi.org/10.1007/3-540-31186-6_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25541-3
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