One-dimensional linear recursions with Markov-dependent coefficients

Abstract

For a class of stationary Markov-dependent sequences $(A_n,B_n)\in {\mathbb{R}}^2,$ we consider the random linear recursion $S_n=A_n+B_n{S}_{n-1},$ $n\in \mathbb{Z},$ and show that the distribution tail of its stationary solution has a power law decay.

Published at http://dx.doi.org/10.1214/105051606000000844 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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