Fractional Ornstein-Uhlenbeck process with stochastic forcing and its applications

TL;DR

This paper studies a fractional Ornstein-Uhlenbeck process with stochastic drift, analyzing its statistical properties, dependence structure, and applications in neuronal modeling, along with simulation methods.

Contribution

It introduces a fractional Ornstein-Uhlenbeck process with stochastic forcing, detailing its mean, covariance, dependence properties, and applications, including simulation algorithms.

Findings

Characterized mean and covariance functions of the process.

Identified conditions for short- and long-range dependence.

Provided simulation algorithms for sample paths.

Abstract

We consider a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractional Brownian motion. For such process we specify mean and covariance functions, concentrating on their asymptotic behavior. This gives us a sort of short- or long-range dependence, under specified hypotheses on the covariance of the forcing process. Applications of this process in neuronal modeling are discussed, providing an example of a stochastic forcing term as a linear combination of Heaviside functions with random center. Simulation algorithms for the sample path of this process are finally given.