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The Stationary Distributions of a Class of Markov Chains
School of Mathematics and Statistics, University of Sheffield, Sheffield, UK
- 1 School of Mathematics and Statistics, University of Sheffield, Sheffield, UK
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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.
KeywordsParker’s ModelMarkov ChainsInteger Sequences
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