Simulation of multi-dimensional random fields by stochastic harmonic functions

Abstract:

The subject of this paper is to propose the stochastic harmonic functions into the multi-dimension, homogeneous, Gaussian random fields. In the first place, it proved that in the two-dimensional random field when the random phase angles and random circular frequencies are independent and uniformly distributed, the amplitude can be obtained by the target power spectral density function and the random circular frequencies specifically. Meanwhile, the power spectral density function is equal to the target one. Then, it proved that stochastic harmonic random field is asymptotic to the normal distribution. In addition, the stochastic harmonic functions can be expanded into multi-dimensional random fields by the uniformed expression in the paper. Finally, several numerical examples are given to clarify the validity of stochastic harmonic function.