Occupation time theorems for one-dimensional random walks and diffusion processes in random environments
type: Item
instance of: scholarly article
title: Occupation time theorems for one-dimensional random walks and diffusion processes in random environments
zbMATH Open document ID: 1161.60025
author: Yuji Kasahara
author: Shinzo Watanabe
published in: Stochastic Processes and their Applications
publication date: 2009-03-10T00:00:00Z
full work available at URL: http://hdl.handle.net/2241/102008
review text: Already at the beginning of the paper the authors develop a general theory for the growth in time, in the log scale, of a class of one-dimensional Brownian additive functionals. These results they apply to obtain asymptotic growth in time of occupation times of a family of one-dimensional diffusion processes. In the next step the authors achieve the long time asymptotics of occupation times for diffusions (and random walks) in random environments. They fundamentally assume that the environment is self-similar in the case of diffusion and asymptotically self-similar in the case of random walks. The environments on the positive and negative sides are independent symmetric stable processes which may have different exponents. The case of random walks is studied by imbedding them in birth-and-death processes with asymptotically self-similar environments.
reviewed by: Elisaveta Pancheva
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60G51
Mathematics Subject Classification ID: 60G52
zbMATH DE Number: 5527423
zbMATH Keywords: occupation times
zbMATH Keywords: arc-sine law
zbMATH Keywords: Lamperti laws
zbMATH Keywords: Brox model
zbMATH Keywords: random environments
zbMATH Keywords: Feller generator
zbMATH Keywords: functional limit theorem
MaRDI profile type: Publication
OpenAlex ID: W2071365545
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DOI: 10.1016/J.SPA.2008.02.005
description: scientific article; zbMATH DE number 5527423