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

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  • Takahashi, Hiroshi
  • Tamura, Yozo

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.

Suggested Citation

  • Takahashi, Hiroshi & Tamura, Yozo, 2023. "Diffusion processes in Brownian environments on disconnected selfsimilar fractal sets in R," Statistics & Probability Letters, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:stapro:v:193:y:2023:i:c:s0167715222002073
    DOI: 10.1016/j.spl.2022.109694
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    References listed on IDEAS

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    1. Makoto Maejima & Ken-iti Sato, 1999. "Semi-Selfsimilar Processes," Journal of Theoretical Probability, Springer, vol. 12(2), pages 347-373, April.
    2. Alves, Samuel B. & de Oliveira, Gilson F. & de Oliveira, Luimar C. & Passerat de Silans, Thierry & Chevrollier, Martine & Oriá, Marcos & de S. Cavalcante, Hugo L.D., 2016. "Characterization of diffusion processes: Normal and anomalous regimes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 392-401.
    3. Alireza Khalili Golmankhaneh & Renat Timergalievich Sibatov, 2021. "Fractal Stochastic Processes on Thin Cantor-Like Sets," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
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