Recurrence and transience properties of multi-dimensional diffusion processes in selfsimilar and semi-selfsimilar random environments

Seiichiro Kusuoka, Hiroshi Takahashi, Yozo Tamura

研究成果: Article査読

1 被引用数 (Scopus)

抄録

We consider d-dimensional diffusion processes in multi-parameter random environments which are given by values at different d points of one-dimensional α-stable or (r, α)-semi-stable Lévy processes. From the model, we derive some conditions of random environments that imply the dichotomy of recurrence and transience for the d-dimensional diffusion processes. The limiting behavior is quite different from that of a d-dimensional standard Brownian motion. We also consider the direct product of a one-dimensional diffusion process in a reflected non-positive Brownian environment and a one-dimensional standard Brownian motion. For the two-dimensional diffusion process, we show the transience property for almost all reflected Brownian environments.

本文言語English
ページ(範囲)1-11
ページ数11
ジャーナルElectronic Communications in Probability
22
DOI
出版ステータスPublished - 2017

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性

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