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One-dimensional linear recursions with Markov-dependent coefficients

Alexander Roitershtein
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Abstract

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

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Alexander Roitershtein. 2007-04-03. One-dimensional linear recursions with Markov-dependent coefficients. https://doi.org/10.1214/105051606000000844

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