Concentration inequalities for Euler schemes
Résumé
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.