Probability Theory and Related Fields

, Volume 88, Issue 1, pp 121–136 | Cite as

Complete convergence theorem for a competition model

  • R. Durrett
  • A. M. Møller


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.


Stochastic Process Probability Theory Stationary Distribution Mathematical Biology Convergence Theorem 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • R. Durrett
    • 1
  • A. M. Møller
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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