Tail of the stationary solution of the stochastic equation \(Y_{n+1}=a_{n} Y_{n}+b_{n}\) with Markovian coefficients

DOI10.1016/j.spa.2005.06.009zbMath1096.60025OpenAlexW1965770373MaRDI QIDQ5921699

Benoîte De Saporta

Publication date: 7 December 2005

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2005.06.009

zbMATH Keywords

spectral radiusMarkov chainnonnegative matricesrandom walkladder heightsrenewal equationstochastic difference equationtail distributionMarkov-switching auto regression

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Stochastic processes (60G99)

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Cites Work

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• Implicit renewal theory and tails of solutions of random equations
• Products of random affine transformations
• Random difference equations and renewal theory for products of random matrices
• Renewal theory for functionals of a Markov chain with general state space
• Renewal theorem for a system of renewal equations
• The tail of the stationary distribution of a random coefficient \(\text{AR}(q)\) model.
• On systems of renewal equations
• Matrix Analysis
• The stochastic equation Y_n+1=A_nY_n + B_n with stationary coefficients
• Applied Probability and Queues

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