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 |
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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