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Complete convergence theorem for a competition model
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  • Published: March 1991

Complete convergence theorem for a competition model

  • R. Durrett1 &
  • A. M. Møller1 

Probability Theory and Related Fields volume 88, pages 121–136 (1991)Cite this article

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  • 10 Citations

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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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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, 14853-7901, Ithaca, NY, USA

    R. Durrett & A. M. Møller

Authors
  1. R. Durrett
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  2. A. M. Møller
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Additional information

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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Cite this article

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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  • Received: 19 March 1990

  • Revised: 20 September 1990

  • Issue Date: March 1991

  • DOI: https://doi.org/10.1007/BF01193585

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Keywords

  • Stochastic Process
  • Probability Theory
  • Stationary Distribution
  • Mathematical Biology
  • Convergence Theorem
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