Convergence theorems for semi-selfsimilar processes induced by random motions in random environments

Hiroshi Takahashi

Convergence theorems for semi-selfsimilar processes induced by random motions in random environments

Research output: Contribution to journal › Article › peer-review

Abstract

We investigated convergence theorems of semi-selfsimilar processes to selfsimilar ones, which are described by stochastic integrals with respect to semi-stable and stable Lévy processes. Typical processes expressed to be such forms are a scaled limit of random walk in random scenery studied by Kesten and Spizter and that of birth and death process in random environment studied by Kawazu and Kesten. We show that their selfsimilar limit processes are provided by semi-selfsimilar processes.

Original language	English
Pages (from-to)	273-284
Number of pages	12
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume	20
Issue number	2
Publication status	Published - 2013 Apr 22
Externally published	Yes

Keywords

Birth and death process in random environment
Local time
Random walk in random scenery
Selfsimilar process
Semi-selfsimilar process

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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abstract = "We investigated convergence theorems of semi-selfsimilar processes to selfsimilar ones, which are described by stochastic integrals with respect to semi-stable and stable L{\'e}vy processes. Typical processes expressed to be such forms are a scaled limit of random walk in random scenery studied by Kesten and Spizter and that of birth and death process in random environment studied by Kawazu and Kesten. We show that their selfsimilar limit processes are provided by semi-selfsimilar processes.",

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AB - We investigated convergence theorems of semi-selfsimilar processes to selfsimilar ones, which are described by stochastic integrals with respect to semi-stable and stable Lévy processes. Typical processes expressed to be such forms are a scaled limit of random walk in random scenery studied by Kesten and Spizter and that of birth and death process in random environment studied by Kawazu and Kesten. We show that their selfsimilar limit processes are provided by semi-selfsimilar processes.

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JO - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

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