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

Hiroshi Takahashi, Yozo Tamura

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Article number109694
JournalStatistics and Probability Letters
Volume193
DOIs
Publication statusPublished - 2023 Feb

Keywords

  • Disconnected selfsimilar fractal set
  • Generalized diffusion process
  • Random environment

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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