One-dimensional linear recursions with Markov-dependent coefficients

Details One-dimensional linear recursions with Markov-dependent coefficients One-dimensional linear recursions with Markov-dependent coefficients

2004-09-19

arxiv.org/abs/math/0409335v2

Annals of Applied Probability 2007, Vol. 17, No. 2, 572-608

Mathematics

Probability

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

Scientific paper

10.1214/105051606000000844

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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