# Boundary effect in competition processes

@article{Shcherbakov2019BoundaryEI, title={Boundary effect in competition processes}, author={Vadim Shcherbakov and Stanislav Volkov}, journal={J. Appl. Probab.}, year={2019}, volume={56}, pages={750-768} }

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.

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Linear competition processes and generalized Pólya urns with removals

- MathematicsStochastic Processes and their Applications
- 2021

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…

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