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.
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