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.
Publié le : 1991-02-14
Classification:
Additive Markov process,
autoregressive conditional heteroscedastice sequence,
composition of random functions,
queues,
random equations,
random recurrence relations,
renewal theory,
Tauberian remainder theory,
60H25,
60K05,
60K25
@article{1177005985,
author = {Goldie, Charles M.},
title = {Implicit Renewal Theory and Tails of Solutions of Random Equations},
journal = {Ann. Appl. Probab.},
volume = {1},
number = {4},
year = {1991},
pages = { 126-166},
language = {en},
url = {http://dml.mathdoc.fr/item/1177005985}
}
Goldie, Charles M. Implicit Renewal Theory and Tails of Solutions of Random Equations. Ann. Appl. Probab., Tome 1 (1991) no. 4, pp. 126-166. http://gdmltest.u-ga.fr/item/1177005985/