Diffusion processes in Brownian environments on disconnected selfsimilar fractal sets in R

Hiroshi Takahashi and Yozo Tamura

Statistics & Probability Letters, 2023, vol. 193, issue C

Abstract: We investigate the limiting behavior of diffusion processes in Brownian environments on disconnected selfsimilar fractal sets in R. Due to the effect of Brownian environments, the diffusion processes exhibit ultra-slow diffusive behavior, which are called Brox-type diffusions. We show that the limiting distributions are given under suitable scalings determined by selfsimilar fractal sets and measures related to the sets. The scaling properties are different from that of the Brox-type diffusion on R.

Keywords: Random environment; Disconnected selfsimilar fractal set; Generalized diffusion process (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2022.109694

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