Skew Brownian diffusions across Koch interfaces

TL;DR

This paper investigates the behavior of skew Brownian motion across fractal Koch interfaces, analyzing how the process's properties change as the interface's thickness and skewness diminish at different rates.

Contribution

It provides a detailed asymptotic analysis of skew Brownian motion across pre-fractal Koch interfaces with varying parameters.

Findings

Asymptotic behavior characterized for different rates of vanishing thickness and skewness.

Insights into the influence of fractal interfaces on stochastic processes.

Potential applications in modeling diffusion across complex boundaries.

Abstract

We consider planar skew Brownian motion (BM) across pre-fractal Koch interfaces $\partial \Omega^n$ and moving on $\overline{\Omega^n} \cup \Sigma^n= \Omega^n_\varepsilon$. We study the asymptotic behaviour of the corresponding multiplicative additive functionals when thickness of $\Sigma^n$ and skewness coefficients vanish with different rates.