The Stationary Distributions of a Class of Markov Chains ()
Abstract
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 Parker’s 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.
Share and Cite:
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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