Homogenization of a Multivariate Diffusion with Semipermeable Interfaces

Olga Aryasova (), Ilya Pavlyukevich () and Andrey Pilipenko ()
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Olga Aryasova: National Academy of Sciences of Ukraine
Ilya Pavlyukevich: Friedrich Schiller University Jena
Andrey Pilipenko: National Academy of Sciences of Ukraine

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1787-1823

Abstract: Abstract We study the homogenization problem for a system of stochastic differential equations with local time terms that models a multivariate diffusion in the presence of semipermeable hyperplane interfaces with oblique penetration. We show that this system has a unique weak solution and determine its weak limit as the distances between the interfaces converge to zero. In the limit, the singular local times terms vanish and give rise to an additional regular interface-induced drift.

Keywords: Local times; Homogenization; Existence and uniqueness of weak solutions; Semipermeable interfaces; Oblique reflection; Weak convergence; Martingale problem; 60H10; 60F05; 60H17; 60J55 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01317-5

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