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February, 1991 Implicit Renewal Theory and Tails of Solutions of Random Equations
Charles M. Goldie
Ann. Appl. Probab. 1(1): 126-166 (February, 1991). DOI: 10.1214/aoap/1177005985

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.

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Charles M. Goldie. "Implicit Renewal Theory and Tails of Solutions of Random Equations." Ann. Appl. Probab. 1 (1) 126 - 166, February, 1991. https://doi.org/10.1214/aoap/1177005985

Information

Published: February, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0724.60076
MathSciNet: MR1097468
Digital Object Identifier: 10.1214/aoap/1177005985

Subjects:
Primary: 60H25
Secondary: 60K05 , 60K25

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

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.1 • No. 1 • February, 1991
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