Journal
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Volume 144, Issue -, Pages 125-152Publisher
ELSEVIER
DOI: 10.1016/j.spa.2021.11.001
Keywords
Birth-and-death process; Competition process; Branching process; Generalized Polya urn with removals; Martingale
Categories
Funding
- Crafoord, Sweden [20190667]
- Swedish Research Council [VR 201904173]
Ask authors/readers for more resources
This paper focuses on studying the long-term behavior of a competition process, showing that eventually only a random subset of non-interacting components survives while others become extinct. Similar results are also applicable to a related generalized Polya urn model with removals.
A competition process is a continuous time Markov chain that can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. This paper is devoted to the study of the long-term behaviour of such a competition process, where a component of the process increases with a linear birth rate and decreases with a rate given by a linear function of other components. A zero is an absorbing state for each component, that is, when a component becomes zero, it stays zero forever (and we say that this component becomes extinct). We show that, with probability one, eventually only a random subset of non-interacting components of the process survives. A similar result also holds for the relevant generalized Polya urn model with removals. (c) 2021 Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available