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A note on the comparison of stationary laws of Markov processes

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  • Pflug, Georg Ch.

Abstract

Let {Xn}, {Yn} be Markov process on k, satisfying Xn+1 = T1(Xn)+Zn, Yn+1 = T2(Yn)+Zn, where {Zn} are i.i.d random variables. Let [mu]X resp. [mu]Y be the stationary distributions of {Xn}resp. {Yn}. We introduce an order relation for probabilities measuring the degree of concentration around zero and derive a result connecting this degree of concentration with properties of the functions Ti and the distribution of {Zn}. Our theorem generalizes a known result for the univariate case which was given by Högnäs (1986).

Suggested Citation

  • Pflug, Georg Ch., 1991. "A note on the comparison of stationary laws of Markov processes," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 331-334, April.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:4:p:331-334
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