Population processes sampled at random times

Abstract

In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are investigated. In particular, we study the hitting times in all cases and examine their long-range behavior. The time-changed population models considered here display upward (Birth process) and downward jumps (death processes) of arbitrary size and, for this reason, can be adopted as adequate models in ecology, epidemics and finance situations, under stress conditions.

19 pages, 3 figures

References in corpus (6)

• Fractional processes: from Poisson to branching one
• Compound Poisson process with a Poisson subordinator
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• Simulation and estimation for the fractional Yule process
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Cited by in corpus (1)

• Properties of Poisson processes directed by compound Poisson-Gamma subordinators