Generation of spatiotemporal correlated noise in 1+1 dimensions

TL;DR

This paper introduces a generalized spatiotemporal correlated noise model in 1+1 dimensions, combining Ornstein-Uhlenbeck processes in time and space, with explicit autocorrelation functions and a numerical simulation algorithm.

Contribution

It presents a new generalized Langevin process with explicit autocorrelation and a simulation method, extending previous models of spatiotemporal noise.

Findings

Derived the autocorrelation function in real space.

Provided a numerical algorithm for simulation.

Compared with existing models for spatiotemporal noise.

Abstract

We propose a generalization of the Ornstein-Uhlenbeck process in 1+1 dimensions which is the product of a temporal Ornstein-Uhlenbeck process with a spatial one and has exponentially decaying autocorrelation. The generalized Langevin equation of the process, the corresponding Fokker-Planck equation, and a discrete integral algorithm for numerical simulation is given. The process is an alternative to a recently proposed spatiotemporal correlated model process [J. Garcia-Ojalvo et al., Phys. Rev. A 46, 4670 (1992)] for which we calculate explicitely the hitherto not known autocorrelation function in real space.