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.
"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