Stationary measures for some Markov chain models in ecology and economics

Athreya, Krishna B. (2003) Stationary measures for some Markov chain models in ecology and economics Economic Theory, 23 (1). p. 107. ISSN 0938-2259

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Official URL: http://www.springerlink.com/content/rc8ra6895vkm1e...

Related URL: http://dx.doi.org/10.1007/s00199-002-0352-1

Abstract

Let F≡ {f:f:[0, ∞) → [0, ∞), f(0) =0,f continuous,lim x↓0 f(x)/x=C exists in (0,∞), 0 < g(x) ≡ f(x)/Cx <1 for x in (0,∞). Let {fj}j≥1 be an i.i.d. sequence from F and X0 be a nonnegative random variable independent of {fj}j≥1. Let {Xn}n≥0 be the Markov chain generated by the iteration of random maps {fj}j≥1by Xn+1=fn+1(Xn), n≥0. Such Markov chains arise in population ecology and growth models in economics. This paper studies the existence of nondegenerate stationary measures for {Xn}. 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).

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Population Models; Random Maps; Markov Chains; Stationary Measures;
ID Code:1150
Deposited On:05 Oct 2010 12:51
Last Modified:16 May 2016 12:18

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