The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 1, Number 1 (1991), 126-166.
Implicit Renewal Theory and Tails of Solutions of Random Equations
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.
Ann. Appl. Probab., Volume 1, Number 1 (1991), 126-166.
First available in Project Euclid: 19 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60H25: Random operators and equations [See also 47B80]
Secondary: 60K05: Renewal theory 60K25: Queueing theory [See also 68M20, 90B22]
Additive Markov process autoregressive conditional heteroscedastice sequence composition of random functions queues random equations random recurrence relations renewal theory Tauberian remainder theory
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