The arcsine law for random walks on the line is well known and it was extended greatly by Lamperti for a class of discrete-time stochastic processes. In the present paper we treat its extreme case where the excursion intervals have very heavy tail probabilities. The result is a refinement of Lamperti’s theorem. A functional limit theorem is also discussed.
"A limit theorem for occupation times of Lamperti’s stochastic processes." Proc. Japan Acad. Ser. A Math. Sci. 84 (1) 15 - 18, January 2008. https://doi.org/10.3792/pjaa.84.15