A Numerical Scheme using Excursion Theory for Simulating Stochastic Differential Equations with Reflection and Local Time at a Boundary

For solving stochastic differential equations there exists a number of numer-ical schemes, e.g. the Euler scheme. If a reflection is considered, most methods have moreor less shortcomings. In this paper we suggest another ansatz of numerical schemes forapproximating the expectation of a functional of a stochastic differential equation directlyincluding a boundary condition with instantaneous reflection. The idea of this approachis to approximate the underlying point process arising by cutting the diffusion at the levelset of the boundary and parametrizing these excursions by the local time. Additionly,this methods is easily to implement on Computers. Furthermore we give the order ofconvergence.