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• W2113752797 abstract "Consider compound Poisson processes with negative drift and no negative jumps, which converge to some spectrally positive Lévy process with nonzero Lévy measure. In this paper, we study the asymptotic behavior of the local time process, in the spatial variable, of these processes killed at two different random times: either at the time of the first visit of the Lévy process to 0, in which case we prove results at the excursion level under suitable conditionings; or at the time when the local time at 0 exceeds some fixed level. We prove that finite-dimensional distributions converge under general assumptions, even if the limiting process is not càdlàg. Making an assumption on the distribution of the jumps of the compound Poisson processes, we strengthen this to get weak convergence. Our assumption allows for the limiting process to be a stable Lévy process with drift. These results have implications on branching processes and in queueing theory, namely, on the scaling limit of binary, homogeneous Crump–Mode–Jagers processes and on the scaling limit of the Processor-Sharing queue length process." @default.
• W2113752797 created "2016-06-24" @default.
• W2113752797 creator A5032948315 @default.
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• W2113752797 date "2013-04-11" @default.
• W2113752797 modified "2023-10-15" @default.
• W2113752797 title "Asymptotic Behavior of Local Times of Compound Poisson Processes with Drift in the Infinite Variance Case" @default.
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• W2113752797 doi "https://doi.org/10.1007/s10959-013-0492-1" @default.
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