Rigorous representation and exact simulation of real Gaussian stationary processes

It is shown that the real Gaussian stationary process with zero mean can be exactly interpreted as a convolution defined by its covariance and a complex white noise plus the conjugate pair of the complex white noise. When the algorithm for generating the white noise is given, such a representation thereby offers a direct and convenient technique to numerically simulate Gaussian processes with arbitrary correlations. Moreover, the fast Fourier transform can be invoked for solving the convolution, which leads to a feasible implementation of the simulation method. As a primary test, a Gaussian process in quantum dissipation is simulated. This stochastic process has an infinitely long correlation time and is hardly treated by other approaches. (C) 2010 Elsevier B.V. All rights reserved.