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Homogenization of a Multivariate Diffusion with Semipermeable Interfaces

Author

Listed:
  • Olga Aryasova

    (National Academy of Sciences of Ukraine
    Friedrich Schiller University Jena
    Igor Sikorsky Kyiv Polytechnic Institute)

  • Ilya Pavlyukevich

    (Friedrich Schiller University Jena)

  • Andrey Pilipenko

    (National Academy of Sciences of Ukraine
    Igor Sikorsky Kyiv Polytechnic Institute)

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.

Suggested Citation

  • Olga Aryasova & Ilya Pavlyukevich & Andrey Pilipenko, 2024. "Homogenization of a Multivariate Diffusion with Semipermeable Interfaces," Journal of Theoretical Probability, Springer, vol. 37(2), pages 1787-1823, June.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:2:d:10.1007_s10959-024-01317-5
    DOI: 10.1007/s10959-024-01317-5
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