Recurrence-Transience Criteria for Storage Processes and Their Applications

Abstract

We obtain sufficient conditions for recurrence and sufficient conditions for transience of storage processes. Applying these results, we give a necessary and sufficient condition for transience in case the input process is a stable process and the release rate is a power function. This result is extended using Abelian theorem for Stieltjes transforms. As another application, we refine conditions for recurrence-transience in case the release rate is non-decreasing and bounded. One of these results corresponds to a recurrence-transience criterion for Bessel processes. As a by-product, the necessary and sufficient condition for transience of processes of Ornstein-Uhlenbeck typeis simplified in diagonal drift coefficient case.