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Comparison Results for Branching Processes in Random Environments

Part of: Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Franco Pellerey
Franco Pellerey*
Affiliation:
Politecnico di Torino
*
∗ Postal address: Dipartimento di Matematica, Politecnico di Torino, corso Duca Degli Abruzzi 24, 10129 Torino, Italy. Email address: franco.pellerey@polito.it
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Abstract

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In this note we consider branching processes whose behavior depends on a dynamic random environment, in the sense that we assume that the offspring distributions of individuals are parametrized, over time, by the realizations of a process describing the environmental evolution. We study how the variability in time of the environment modifies the variability of total population by considering two branching processes of this kind (but subjected to different environments). We also provide conditions on the random environments in order to stochastically compare their marginal distributions in the increasing convex sense. Weaker conditions are also provided for comparisons at every fixed time of the expected values of the two populations.

Keywords

Branching processincreasing convex ordersupermodular orderconcordance order

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 60G99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007 , pp. 142 - 150
Copyright
Copyright © Applied Probability Trust 2007 

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