TY - JOUR
T1 - Diffusion processes in Brownian environments on disconnected selfsimilar fractal sets in R
AU - Takahashi, Hiroshi
AU - Tamura, Yozo
N1 - Funding Information:
The authors would like to express their profound gratitude to Professor Y. Suzuki for her useful comments on the original manuscript. The authors also thank the anonymous referees for their careful reading of the manuscript. The research of H. Takahashi is supported by JSPS, Japan KAKENHI Grant Number 18K03324 . The authors also thank Edanz ( https://jp.edanz.com/ac ) for editing a draft of this manuscript.
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2023/2
Y1 - 2023/2
N2 - 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.
AB - 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.
KW - Disconnected selfsimilar fractal set
KW - Generalized diffusion process
KW - Random environment
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U2 - 10.1016/j.spl.2022.109694
DO - 10.1016/j.spl.2022.109694
M3 - Article
AN - SCOPUS:85141312836
SN - 0167-7152
VL - 193
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
M1 - 109694
ER -