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The Stationary Distributions of a Class of Markov Chains

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DOI: 10.4236/am.2013.45105    3,295 Downloads   5,150 Views   Citations
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The objective of this paper is to find the stationary distribution of a certain class of Markov chains arising in a biological population involved in a specific type of evolutionary conflict, known as Parkers model. In a population of such players, the result of repeated, infrequent, attempted invasions using strategies from{0,1,2,,m-1}, is a Markov chain. The stationary distributions of this class of chains, for m ε {3,4,,} are derived in terms of previously known integer sequences. The asymptotic distribution (for m →∞) is derived.

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The authors declare no conflicts of interest.

Cite this paper

C. Cannings, "The Stationary Distributions of a Class of Markov Chains," Applied Mathematics, Vol. 4 No. 5, 2013, pp. 769-773. doi: 10.4236/am.2013.45105.


[1] M. Broom and C. Cannings, “Evolutionary Game Theory,” In: Encyclopedia of Life Sciences, John Wiley & Sons Ltd, Chichester, 2010.
[2] G. A. Parker, “Sexual Selection and Sexual Conflict,” In: M. S. Blum and N. A. Blum, Eds., Sexual Selection and Reproductive Competition, Academic Press, New York, 1979, pp. 123-166.
[3] C. Cannings, “Populations Playing Parker’s Model,” In: Preparation.
[4] J. Norris, “Markov Chains,” Cambridge University Press, Cambridge, 1998.
[5] “The On-Line Encyclopedia of Integer Sequences.”

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