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We prove several properties of the EMCEL scheme, which is capable ofapproximating one-dimensional continuous strong Markov processes indistribution on the path space (the scheme is briefly recalled). Special casesinclude irregular stochastic differential equations and processes with stickyfeatures. In particular, we highlight differences from the Euler scheme in thecase of stochastic differential equations and discuss a certain "stabilizing"behavior of the EMCEL scheme like "smoothing and tempered growth behavior".

Properties of the EMCEL scheme for approximating irregular diffusions