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On Wong-Zakai type approximations of reflected diffusions. (English) Zbl 1325.60097

Summary: We study weak and strong convergence of Wong-Zakai type approximations of reflected stochastic differential equations on general domains satisfying the conditions (A) and (B) introduced by P.-L. Lions and A. S. Sznitman [Commun. Pure Appl. Math. 37, No. 4, 511–537 (1984; Zbl 0598.60060)]. We assume that the diffusion coefficient is Lipschitz continuous, but the drift coefficient need not be even continuous. In the case where the drift coefficient is also Lipschitz continuous, we show that the rate of convergence is exactly the same as for the usual Euler type approximation.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
60J60 Diffusion processes
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60G17 Sample path properties

Citations:

Zbl 0598.60060
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