One-dimensional linear recursions with Markov-dependent coefficients

One-dimensional linear recursions with Markov-dependent coefficients

Alexander Roitershtein

Source: Ann. Appl. Probab. Volume 17, Number 2 (2007), 572-608.

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.

Primary Subjects: 60K15

Secondary Subjects: 60K20

Keywords: Random linear recursions; stochastic difference equations; tail asymptotic; Markov random walks; Markov renewal theory

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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1174323257
Digital Object Identifier: doi:10.1214/105051606000000844
Mathematical Reviews number (MathSciNet): MR2308336
Zentralblatt MATH identifier: 1125.60092

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