Simulation of stochastic processes with known correlation functions

Abstract

Abstract A procedure for the simulation of normal stochastic processes with specified correlation functions is developed and described in detail. A known function is fitted to the given correlation by least-squares optimisation and is then employed to determine the form of a random number generator, which is the source of the random shift parameters in a set of broken line processes with ordinates determined from zero mean normal distributions. For a given number of such processes, the domain of their correlation functions and the variances of the normal distributions are also determined by the initial optimisation. The sum of the resulting broken line processes is the required simulated process. Any point on this process can be individually simulated, without the need to store large numbers of generated process values, so that the method is suitable for use on microcomputers. Large numbers of points can be generated quickly, as most process parameters are determined before the simulation run. The procedure is therefore suitable for the construction of other processes in the simulation of outcrossing problems in reliability theory.