Stationary measures for some Markov chain models in ecology and economics期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Stationary measures for some Markov chain models in ecology and economics

Authors:	Athreya Krishna B.

Affiliation:	(1) School of Operations Research and Industrial Engineering, Cornell University, NY 14853 Ithaca, USA

Abstract:	Summary. Let continuous, $limlimits_{x downarrow 0} frac{f(x)}{x} = C$ exists in $(0, infty), 0 < g (x) equiv frac{f(x)}{C x} < 1$ for x in . Let ${f_j}_{j geq 1}$ be an i.i.d. sequence from F and X₀ be a nonnegative random variable independent of ${f_j}_{j geq 1}$ . Let ${X_n}_{n geq 0}$ be the Markov chain generated by the iteration of random maps ${f_j}_{j geq 1}$ by $X_{n + 1} = f_{n + 1} (X_n), n geq 0$ . Such Markov chains arise in population ecology and growth models in economics. This paper studies the existence of nondegenerate stationary measures for {X_n}. A set of necessary conditions and two sets of sufficient conditions are provided. There are some convergence results also. The present paper is a generalization of the work on random logistics maps by Athreya and Dai (2000).Received: 20 March 2002, Revised: 4 December 2002, JEL Classification Numbers: C22, D9.The author wishes to thank Professor Mukul Majumdar and the referees for several useful suggestions.

Keywords:	Population models Random maps Markov chains Stationary measures.
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