Rate of Convergence of Implicit Approximations for stochastic evolution equations

Istvan Gyöngy (1) , Annie Millet (2, 3, 4)

1 School of Mathematics - University of Edinburgh
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 CES - Centre d'économie de la Sorbonne
4 SAMOS - Statistique Appliquée et MOdélisation Stochastique

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators are considered. Under some regularity condition assumed for the solution, the rate of convergence of implicit Euler approximations is estimated under strong monotonicity and Lipschitz conditions. The results are applied to a class of quasilinear stochastic PDEs of parabolic type.

Mots clés: Stochastic evolution equations; Monotone operators; coercivity; implicit approximations

Domaines: Probabilités [math.PR]

Istvan Gyöngy, Annie Millet. Rate of Convergence of Implicit Approximations for stochastic evolution equations. Peter H. Baxendale, Sergey V. Lototsky. Stochastic Differential Equations: Theory and Applications : A Volume in Honor of Professor Boris L Rozovskii, World Scientific, pp.281-310, 2007, Interdisciplinary Mathematical Sciences. ⟨hal-00080707v2⟩