Boundary value problems

Anomalous Phenomena on Regular and Irregular Domains: Approximating Complexity for the Applied Sciences

We aim to find new results in Probability, Analysis and Statistics concerning motions on regular and irregular domains with reflection on regular and irregular regions of the domains. By reflection we mean elastic (Robin), slow (sticky) and skew (transmission) reflection. By “irregular domain” we mean “fractal domain” and “domain with fractal boundary or fractal interface”. Our analysis includes the connections between fractional dimension (irregular domains) and fractional calculus, that is equations involving fractional (or non-local) operators.

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Skew brownian diffusions across koch interfaces

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