Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications

Giacomo Ascione (), Yuliya Mishura () and Enrica Pirozzi ()
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Giacomo Ascione: Università di Napoli FEDERICO II
Yuliya Mishura: Taras Shevchenko National University of Kyiv
Enrica Pirozzi: Università di Napoli FEDERICO II

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 1, 53-84

Abstract: 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 given.

Keywords: Fractional Brownian motion; Fractional Ornstein-Uhlenbeck process; Forcing term; Covariance function; Asymptotic behavior; Correlated processes; Leaky integrate-and-fire neuronal model; 60G22; 60G15; 68U20 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-019-09748-y

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