Abstract
In this paper we give a simple construction of the general stationary regenerative set, based on the stationary version of the associated subordinator (increasing Levy process). We show that, in a certain sense, the closed range of such a Levy process is a stationary regenerative subset of $\mathbb{R}$. The distribution of this regenerative set is $\sigma$-finite in general; it is finite $\operatorname{iff}$ the increments of the Levy process have finite expectation.
Citation
P. J. Fitzsimmons. Michael Taksar. "Stationary Regenerative Sets and Subordinators." Ann. Probab. 16 (3) 1299 - 1305, July, 1988. https://doi.org/10.1214/aop/1176991692
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