Inverse-transformation algorithms for some common stochastic processes

Abstract

Realizations from common stochastic processes are often used by simulation-methodology researchers in Monte Carlo performance evaluation of new and existing methods for output analysis, variance reduction, and optimization. Typically realizations can be obtained easily from either the definition or simple properties of the process. We discuss using the inverse of the distribution function for generating realizations from some of these processes. The inverse transformation always possesses the advantage of correlation induction, useful for variance reduction. We consider the discrete-time processes ARMA, EAR, M/M/1-QT (time in queue), and M/M/I-ST (time in system, the sojourn time), and Markov chains. The inversetransformation algorithms are sometimes slower (e.g., ARMA, M/M/I-ST), sometimes faster (e.g., M/M/1-QT), and often about the same speed as the usual algorithm. Some Fortran implementations are provided.