TITLE:
The Stationary Distributions of a Class of Markov Chains
AUTHORS:
Chris Cannings
KEYWORDS:
Parker’s Model; Markov Chains; Integer Sequences
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.5,
May
13,
2013
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.