Boundary effect in competition processes

Vadim Shcherbakov, Stanislav Volkov

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This paper is devoted to studying the long-term behaviour of a continuous time
Markov chain that can be interpreted as a pair of linear birth processes which
evolve with a competitive interaction; as a special case, they include the famous
Lotka-Volterra interaction. Another example of our process is related to urn
models with ball removals. We show that, with probability one, the process
eventually escapes to innity by sticking to the boundary in a rather unusual
Original languageEnglish
Pages (from-to)750-768
Number of pages19
JournalJournal of Applied Probability
Issue number3
Publication statusPublished - 1 Oct 2019

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