Some new results on the initial transient problem

This paper contains two new results pertaining to the initial transient problem for steady-state simulations. Our first result rigorously establishes the asymptotic superiority of a few long replications relative to a large number of shorter replications, assuming that no initial transient deletion is attempted. Our second result concerns an initial transient detection test proposed by Schruben; we develop asymptotics that are suggestive of the types of initial transients that the test is capable of detecting. As one might expect, the ability to detect a non-stationarity in the simulation output depends both on the magnitude of the non-stationarity of the initial condition, and the degree of autocorrelation in the process.