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Potential Analysis

, Volume 46, Issue 3, pp 431–461 | Cite as

Skew Brownian Diffusions Across Koch Interfaces

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Abstract

We consider planar skew Brownian motion (BM) across pre-fractal Koch interfaces Ω n and moving on \(\overline {{\Omega }^{n}} \cup {\Sigma }^{n}= {\Omega }^{n}_{\varepsilon }\) where Σ n is a suitable neighbourhood of Ω n . We study the asymptotic behaviour of the corresponding multiplicative functionals when thickness of Σ 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.

Keywords

Brownian motion Additive functionals Boundary value problems Fractals 

Mathematics Subject Classifications (2010)

60J65 60J55 35J25 28A80 

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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Dipartimento di Scienze di Base e Applicate per l’Ingegneria“Sapienza” Università di RomaRomaItaly

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