Summary
In this paper we consider a hierarchical competition model. Durrett and Swindle have given sufficient conditions for the existence of a nontrivial stationary distribution. Here we show that under a slightly stronger condition, the complete convergence theorem holds and hence there is a unique nontrivial stationary distribution.
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Partially supported by the National Science Foundation, the National Security Agency, and the Army Research Office through the Mathematical Sciences Institute at Cornell University
Partially supported by the Danish Research Academy
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Durrett, R., Møller, A.M. Complete convergence theorem for a competition model. Probab. Th. Rel. Fields 88, 121–136 (1991). https://doi.org/10.1007/BF01193585
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DOI: https://doi.org/10.1007/BF01193585
Keywords
- Stochastic Process
- Probability Theory
- Stationary Distribution
- Mathematical Biology
- Convergence Theorem