ON THE SIMULATION OF STOCHASTIC-PROCESSES BY SPECTRAL REPRESENTATION

In this paper, a modification in the simulation formula for generating stationary stochastic processes, using the spectral representation me thod developed by Shinozuka, is presented. It is shown that with this modification, the ensemble and temporal autocorrelation function of th e simulated stochastic process for fixed values of time lag 7 converge to their target autocorrelation function much more quickly. If the sa mple function is synthesized with N frequencies, then the rate of the convergence is of the order 1/N-4 instead of 1/N for the original simu lation formula. However, for the whole simulation time T-0, the conver gences of the autocorrelation functions are not uniform for the time l ag tau throughout the range from 0 to T-0/2. It turns out that the pro posed modified simulation formula is preferable for the time lag \tau\ less than or equal to T-0/2 pi and the original simulation formula is preferable for the time lag T-0/2 pi < \tau\ less than or equal to T-0 /2. (C) 1997 Elsevier Science Ltd.