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Boundary effect in competition processes

  • Vadim Shcherbakov (a1) and Stanislav Volkov (a2)


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 removal. We show that, with probability one, the process eventually escapes to infinity by sticking to the boundary in a rather unusual way.


Corresponding author

*Postal address: Department of Mathematics, Royal Holloway, University of London, Egham TW20 0EX, UK.
***Postal address: Centre for Mathematical Sciences, Lund University, SE-221 00 Lund, Sweden.
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