One-dimensional linear recursions with Markov-dependent coefficients

Alexander Roitershtein

doi:10.1214/105051606000000844

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Home > Journals > Ann. Appl. Probab. > Volume 17 > Issue 2 > Article

April 2007 One-dimensional linear recursions with Markov-dependent coefficients

Alexander Roitershtein

Ann. Appl. Probab. 17(2): 572-608 (April 2007). DOI: 10.1214/105051606000000844

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Abstract

For a class of stationary Markov-dependent sequences (A_n, B_n)∈ℝ², we consider the random linear recursion S_n=A_n+B_nS_n−1, n∈ℤ, and show that the distribution tail of its stationary solution has a power law decay.

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Alexander Roitershtein. "One-dimensional linear recursions with Markov-dependent coefficients." Ann. Appl. Probab. 17 (2) 572 - 608, April 2007. https://doi.org/10.1214/105051606000000844

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Published: April 2007

First available in Project Euclid: 19 March 2007

zbMATH: 1125.60092

MathSciNet: MR2308336

Digital Object Identifier: 10.1214/105051606000000844

Subjects:

Primary: 60K15

Secondary: 60K20

Keywords: Markov random walks , Markov renewal theory , Random linear recursions , stochastic difference equations , Tail asymptotic

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Vol.17 • No. 2 • April 2007

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Alexander Roitershtein "One-dimensional linear recursions with Markov-dependent coefficients," The Annals of Applied Probability, Ann. Appl. Probab. 17(2), 572-608, (April 2007)

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