2016/02/16 by N.J. Starreveld, Starreveld, N. J., René Bekker +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1602.05131
openalex publication_date 2016/02/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
This paper presents a set of results relating to the occupation time α(t) of a process X(⋅). The first set of results concerns exact characterizations of α(t) for t≥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 α(t)/t converges to a zero-mean Normal random variable as t→∞) and the tail asymptotics of P(α(t)/t≥ 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.