One-dimensional linear recursions with Markov-dependent coefficients

Alexander Roitershtein

doi:10.1214/105051606000000844

One-dimensional linear recursions with Markov-dependent coefficients

Probability 2007-05-23 v2

Authors: 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.

Keywords

markov chain markov processes

Cite

@article{arxiv.math/0409335,
  title  = {One-dimensional linear recursions with Markov-dependent coefficients},
  author = {Alexander Roitershtein},
  journal= {arXiv preprint arXiv:math/0409335},
  year   = {2007}
}

Comments

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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