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

Slominski, Leszek

Electron. J. Probab. 19, Paper No. 118, 15 p. (2014).

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

Keywords:

reflected stochastic differential equations; reflected diffusions; Wong-Zakai type approximations

Citations:

Zbl 0598.60060