A decomposable branching process in a Markovian environment
Vladimir Vatutin, Elena Dyakonova, Peter Jagers, and Serik Sagitov
TL;DR
This paper analyzes a two-island population model with different environmental conditions, focusing on the survival probabilities in critical and subcritical regimes, considering migration from a variable to a constant environment.
Contribution
It introduces a decomposable branching process model in a Markovian environment with asymmetric migration and derives asymptotic survival probabilities.
Findings
Survival probability decays at specific rates in critical cases.
Migration influences survival chances significantly.
Asymptotic formulas are provided for different regimes.
Abstract
A population has two types of individuals, each occupying an island. One of those, where individuals of type 1 live, offers a variable environment. Type 2 individuals dwell on the other island, in a constant environment. Only one-way migration (1->2) is possible. We study the asymptotics of the survival probability in critical and subcritical cases.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Markov Chains and Monte Carlo Methods · Bayesian Methods and Mixture Models