Boundary effect in competition processes
Abstract
This paper studies the long-term behaviour of a continuous time Markov chain formed by two non-negative integer valued components that evolve subject to a competitive interaction. In the absence of interaction the Markov chain is just a pair of independent linear birth processes with immigration. Interactions of interest include, as a special case, the famous Lotka-Volterra interaction. The Markov chain with another special case of interaction can be interpreted as an urn model with ball removals and is reminiscent, in a sense, of Friedman's urn model. We show that, with probability one, eventually one of the components of the process tends to infinity, while the other component oscillates between values and (between values and in a special case).
Cite
@article{arxiv.1801.09875,
title = {Boundary effect in competition processes},
author = {Vadim Shcherbakov and Stanislav Volkov},
journal= {arXiv preprint arXiv:1801.09875},
year = {2019}
}