An algorithm for on-the-fly generation of samples of non-stationary Gaussian processes based on a sampling theorem

Abstract

A Monte Carlo algorithm is developed for generating samples of real-valued non-stationary Gaussian processes. The method is based on a generalized version of Shannon's sampling theorem for bandlimited deterministic signals, as well as an efficient algorithm for generating conditional Gaussian variables. One feature of the method that is attractive for engineering applications involving stochastic loads is the ability of the algorithm to be implemented “on-the-fly” meaning that, given the value of the sample of the process at the current time step, it provides the value for the sample of the process at the next time step. Theoretical arguments are supported by numerical examples demonstrating the implementation, efficiency, and accuracy of the proposed Monte Carlo simulation algorithm.