Multivalued Stochastic Differential Equations: Convergence of a Numerical Scheme |
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| Authors: | Fré dé ric Bernardin |
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| Affiliation: | (1) Département Génie Civil et Bâtiment, Laboratoire Géomatériaux, Ecole Nationale des Travaux Publics de l'Etat, URA 1652 CNRS, Rue Maurice Audin, 69518 Vaulx-en-Velin Cedex, France;(2) UMR 5585 CNRS, MAPLY, Laboratoire de mathématiques appliquées de Lyon, Université Claude Bernard Lyon I, 69622 Villeurbanne Cedex, France |
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| Abstract: | In this paper we show the strong mean square convergence of a numerical scheme for a Rd-multivalued stochastic differential equation: dXt+A(Xt) dt b(t,Xt)dt+ (t,Xt)dWt and obtain the rate of convergence O(( log(1/)1/2) when the diffusion coefficient is bounded. By introducing a discrete Skorokhod problem, we establish Lp-estimates (p 2) for the solutions and prove the convergence by using a deterministic result. Numerical experiments for the rate of convergence are presented. |
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| Keywords: | stochastic differential equations maximal monotone operators numerical scheme Skorokhod problem numerical experiments |
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