Potential Analysis

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

Skew Brownian Diffusions Across Koch Interfaces



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.


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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