Skew Brownian Diffusions Across Koch Interfaces

摘要

We consider planar skew Brownian motion (BM) across pre-fractal Koch interfaces a,Omega (n) and moving on where I pound (n) is a suitable neighbourhood of a,Omega (n) . We study the asymptotic behaviour of the corresponding multiplicative functionals when thickness of I pound (n) and skewness coefficients vanish with different rates. Thus, we provide a probabilistic framework for studying diffusions across semi-permeable pre-fractal (and fractal) layers and the asymptotic analysis concerning the insulating fractal layer case.