A note on the comparison of stationary laws of Markov processes

Georg Ch. Pflug

Statistics & Probability Letters, 1991, vol. 11, issue 4, 331-334

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).

Keywords: Markov; processes; non-linear; multivariate; autoregressive; processes; degree; of; concentration; comparison; theorem (search for similar items in EconPapers)
Date: 1991
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