Exact numerical simulation of power-law noises

Abstract

Many simulations of stochastic processes require colored noises: I describe here an exact numerical method to simulate power-law noises: the method can be extended to more general colored noises, and is exact for all time steps, even when they are unevenly spaced [as may often happen for astronomical data; see, e.g., N. R. Lomb, Astrophys. Space Sci. 39, 447 (1976)]. The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity.