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Population models at stochastic times

Part of: Stochastic processes

Published online by Cambridge University Press:  10 June 2016

Enzo Orsingher ,
Costantino Ricciuti  and
Bruno Toaldo
Enzo Orsingher*
Affiliation:
Sapienza University of Rome
Costantino Ricciuti*
Affiliation:
Sapienza University of Rome
Bruno Toaldo*
Affiliation:
Sapienza University of Rome
*
* Postal address: Department of Statistical Sciences, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy.
* Postal address: Department of Statistical Sciences, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy.
* Postal address: Department of Statistical Sciences, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy.
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Abstract

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In this paper we consider time-changed models of population evolution Xf(t) = X(Hf(t)), where X is a counting process and Hf is a subordinator with Laplace exponent f. In the case where X is a pure birth process, we study the form of the distribution, the intertimes between successive jumps, and the condition of explosion (also in the case of killed subordinators). We also investigate the case where X represents a death process (linear or sublinear) and study the extinction probabilities as a function of the initial population size n0. Finally, the subordinated linear birth–death process is considered. Special attention is devoted to the case where birth and death rates coincide; the sojourn times are also analysed.

Keywords

Nonlinear birth processsublinear death processlinear death processsojourn timefractional birth processrandom time

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 60G55: Point processes

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 2 , June 2016 , pp. 481 - 498
Copyright
Copyright © Applied Probability Trust 2016 

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