Method for generating two coupled Gaussian stochastic processes

TL;DR

This paper introduces a novel method to generate two coupled Gaussian stochastic processes with arbitrary correlations, extending existing techniques and applicable to fractional Brownian motions and Gaussian random fields.

Contribution

A new Fourier filtering-based method for creating coupled Gaussian processes with customizable correlation functions is proposed, broadening modeling capabilities.

Findings

Successfully generates coupled fractional Brownian motions.

Extends applicability to Gaussian random fields.

Proves robustness of the method.

Abstract

Most processes in nature are coupled; however, extensive null models for generating such processes still lacks. We present a new method to generate two coupled Gaussian stochastic processes with arbitrary correlation functions. This method is developed by modifying the Fourier filtering method. The robustness of this method is proved by generating two coupled fractional Brownian motions and extending its range of application to Gaussian random fields.