Stationary measures for some Markov chain models in ecology and economics
- Athreya, Krishna B.
DOIAbstract
Let F≡ {f:f:[0, ∞) → [0, ∞), f(0) =0,f continuous,lim <SUB>x↓0</SUB> f(x)/x=C exists in (0,∞), 0 < g(x) ≡ f(x)/Cx <1 for x in (0,∞). Let {fj}<SUB>j≥1</SUB> be an i.i.d. sequence from F and X<SUB>0</SUB> be a nonnegative random variable independent of {fj}<SUB>j≥1</SUB>. Let {X<SUB>n</SUB>}<SUB>n≥0</SUB> be the Markov chain generated by the iteration of random maps {fj}<SUB>j≥1</SUB>by X<SUB>n+1</SUB>=f<SUB>n+1</SUB>(X<SUB>n</SUB>), n≥0. Such Markov chains arise in population ecology and growth models in economics. This paper studies the existence of nondegenerate stationary measures for {X<SUB>n</SUB>}. A set of necessary conditions and two sets of sufficien...
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