Approximations for stochastic differential equations with reflecting convex boundaries

Abstract

We consider convergence of a recursive projection scheme for a stochastic differential equation reflecting on the boundary of a convex domain G. If G satisfies Condition (B) in Tanaka (1979), we obtain mean square convergence, pointwise, with the rate O((δ log 1 δ ) 1 2 ) , and if G is a convex polyhedron we obtain mean square convergence, uniformly on compacts, with the rate O(δ log 1 δ ) . An application is given for stochastic differential equations with hysteretic components.