We investigate a multi-type Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Suppose that the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices has negative mean and assuming some additional conditions, we find the asymptotics of the survival probability at time $n$ as $n \to \infty$.

Volume: DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science

Section: Proceedings

Published on: January 1, 2008

Imported on: May 10, 2017

Keywords: branching processes in random environment,survival probability,limit theorems,random walks,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]

References

3 Documents citing this article

Vladimir A. Vatutin;Elena E. Dyakonova, 2021, Properties of multitype subcritical branching processes in random environment, arXiv (Cornell University), 31, 5, pp. 367-382, 10.1515/dma-2021-0032, https://arxiv.org/abs/2007.02289.

Martin P.W. Zerner, 2018, Recurrence and transience of contractive autoregressive processes and related Markov chains, Electronic Journal of Probability, 23, none, 10.1214/18-ejp152, https://doi.org/10.1214/18-ejp152.

2017, Bibliography, Discrete Time Branching Processes in Random Environment, pp. 275-284, 10.1002/9781119452898.biblio.