The Stationary Distributions of a Class of Markov Chains


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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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.

Conflicts of Interest

The authors declare no conflicts of interest.


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[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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