A second order limit law for occupation times of the Cauchy process

Abstract

The purpose of this note is to extend a second order limit law for one dimensional Cauchy process obtained in Kasahara (Y. Kasahara, Limit theorems for occupation times of Markov processes, Publ. RIMS, Kyoto Univ. 12 (1977), pp. 801–818), using the method of moments and some kind of chaining argument.