Properties of the EMCEL scheme for approximating irregular diffusions

Abstract

We prove several properties of the EMCEL scheme, which is capable of approximating one-dimensional continuous strong Markov processes in distribution on the path space (the scheme is briefly recalled). Special cases include irregular stochastic differential equations and processes with sticky features. In particular, we highlight differences from the Euler scheme in the case of stochastic differential equations and discuss a certain “stabilizing” behavior of the EMCEL scheme like “smoothing and tempered growth behavior”.