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Density approximation and exact simulation of random variables that are solutions of fixed-point equations

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  01 July 2016

Luc Devroye  and
Ralph Neininger
Luc Devroye*
Affiliation:
McGill University
Ralph Neininger*
Affiliation:
McGill University
*
∗ Postal address: School of Computer Science, McGill University, 3480 University Street, Montreal, Canada H3A 2K6.
∗ Postal address: School of Computer Science, McGill University, 3480 University Street, Montreal, Canada H3A 2K6.
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Abstract

An algorithm is developed for exact simulation from distributions that are defined as fixed points of maps between spaces of probability measures. The fixed points of the class of maps under consideration include examples of limit distributions of random variables studied in the probabilistic analysis of algorithms. Approximating sequences for the densities of the fixed points with explicit error bounds are constructed. The sampling algorithm relies on a modified rejection method.

Keywords

Random variate generationfixed-point equationperfect simulationrejection methodMonte Carlo method

MSC classification

Primary: 65C10: Random number generation
Secondary: 65C05: Monte Carlo methods 68U20: Simulation 11K45: Pseudo-random numbers; Monte Carlo methods
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 2 , June 2002 , pp. 441 - 468
Copyright
Copyright © Applied Probability Trust 2002 

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