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Concentration Inequalities for Euler Schemes

In: Monte Carlo and Quasi-Monte Carlo Methods 2004

Author

Listed:
  • Florent Malrieu

    (IRMAR)

  • Denis Talay

    (INRIA Sophia-Antipolis)

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.

Suggested Citation

  • Florent Malrieu & Denis Talay, 2006. "Concentration Inequalities for Euler Schemes," Springer Books, in: Harald Niederreiter & Denis Talay (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2004, pages 355-371, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-31186-7_21
    DOI: 10.1007/3-540-31186-6_21
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