On the finite approximation of a Gaussian process and its effect on extreme value theory

► We evaluate the error associated with the finite approximation of a Gaussian process. ► We first examine the limiting case of harmonic components with identical amplitudes. ► We then extend the approach to an arbitrary set of amplitudes using a FFT algorithm. ► With a practical example, we suggest sufficiency conditions for the approximation. ► Alternate approximations of a Gaussian process and their challenges are discussed.