The Annals of Applied Probability

Implicit Renewal Theory and Tails of Solutions of Random Equations

Charles M. Goldie

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Abstract

For the solutions of certain random equations, or equivalently the stationary solutions of certain random recurrences, the distribution tails are evaluated by renewal-theoretic methods. Six such equations, including one arising in queueing theory, are studied in detail. Implications in extreme-value theory are discussed by way of an illustration from economics.

Article information

Source
Ann. Appl. Probab., Volume 1, Number 1 (1991), 126-166.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005985

Digital Object Identifier
doi:10.1214/aoap/1177005985

Mathematical Reviews number (MathSciNet)
MR1097468

Zentralblatt MATH identifier
0724.60076

JSTOR
links.jstor.org

Subjects
Primary: 60H25: Random operators and equations [See also 47B80]
Secondary: 60K05: Renewal theory 60K25: Queueing theory [See also 68M20, 90B22]

Keywords
Additive Markov process autoregressive conditional heteroscedastice sequence composition of random functions queues random equations random recurrence relations renewal theory Tauberian remainder theory

Citation

Goldie, Charles M. Implicit Renewal Theory and Tails of Solutions of Random Equations. Ann. Appl. Probab. 1 (1991), no. 1, 126--166. doi:10.1214/aoap/1177005985. https://projecteuclid.org/euclid.aoap/1177005985


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