Occupation times of alternating renewal processes with L\'evy   applications
  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 $t\geq0$, 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 $t\rightarrow\infty$) and the tail asymptotics of $P(\alpha(t)/t\geq q)$. We apply our findings to spectrally positive L\'evy processes reflected at the infimum and establish various new occupation time results for the corresponding model. 
N. J. Starreveld, R. Bekker, M. Mandjes
math.PR