Abstract
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
way.
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
way.
| Original language | English |
|---|---|
| Pages (from-to) | 750-768 |
| Number of pages | 19 |
| Journal | Journal of Applied Probability |
| Volume | 56 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Oct 2019 |