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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)273-284
Number of pages12
JournalDynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume20
Issue number2
Publication statusPublished - 2013 Apr 22
Externally publishedYes

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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