Abstract
Two functional limit theorems for occupation times of Lamperti’s stochastic processes are established. One is a generalization of Lamperti’s result in 1957 in the null recurrent case, and the other is a limit theorem for the fluctuation in the positively recurrent case. The proofs are based on a limit theorem for i.i.d. random variables with common distribution function belonging to the domain of attraction of a stable law.
Citation
Etsuko Fujihara. Yumi Kawamura. Yuko Yano. "Functional limit theorems for occupation times of Lamperti’s stochastic processes in discrete time." J. Math. Kyoto Univ. 47 (2) 429 - 440, 2007. https://doi.org/10.1215/kjm/1250281054
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