Occupation time theorems for one-dimensional random walks and diffusion processes in random environments

Yuji Kasahara and Shinzo Watanabe

Stochastic Processes and their Applications, 2009, vol. 119, issue 2, 347-372

Abstract: The long time asymptotics of the time spent on the positive side are discussed for one-dimensional diffusion processes in random environments. The limiting distributions under the log-log scale are obtained for the diffusion processes in the stable medium as well as for the Brox model. Similar problems are discussed for random walks in random environments and it is proved that the limiting laws are the same as in the case of diffusions.

Keywords: primary; 60J55 secondary; 60J60; 60G51; 60G52 Occupation times Arc-sine law Lamperti laws Brox model Random environments Feller generator Functional limit theorem (search for similar items in EconPapers)
Date: 2009
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