Occupation times of alternating renewal processes with Lévy applications

Abstract

This paper presents a set of results relating to the occupation time $\alpha (t)$ of a process $X(\cdot )$. The first set of results concerns exact characterizations of $\alpha (t)$ for $t\ge 0$, e.g., in terms of its transform up to an exponentially distributed epoch. In addition we establish a central limit theorem (entailing that a centered and normalized version of $\alpha (t)/t$ converges to a zero-mean Normal random variable as $t\to \infty$) and the tail asymptotics of $P(\alpha (t)/t\ge q)$. We apply our findings to spectrally positive Lévy processes reflected at the infimum and establish various new occupation time results for the corresponding model.

23 pages, 1 figure

References in corpus (1)

• Occupation times for the finite buffer fluid queue with phase-type ON-times

Cited by in corpus (2)

• The $W,Z$ scale functions kit for first passage problems of spectrally negative Levy processes, and applications to the optimization of dividends
• Occupation times for the finite buffer fluid queue with phase-type ON-times