Fractional integral equations and state space transforms

Boris Buchmann; Claudia Klüppelberg

doi:10.3150/bj/1151525129

June 2006 Fractional integral equations and state space transforms

Boris Buchmann, Claudia Klüppelberg

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Bernoulli 12(3): 431-456 (June 2006). DOI: 10.3150/bj/1151525129

Abstract

We introduce a class of stochastic differential equations driven by fractional Brownian motion which allow for a constructive method in order to obtain stationary solutions. This leads to a substantial extension of the fractional Ornstein-Uhlenbeck processes. Structural properties of this class of new models are investigated, and their stationary densities are explicitly given.

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Boris Buchmann. Claudia Klüppelberg. "Fractional integral equations and state space transforms." Bernoulli 12 (3) 431 - 456, June 2006. https://doi.org/10.3150/bj/1151525129

Information

Published: June 2006

First available in Project Euclid: 28 June 2006

zbMATH: 1114.60048

MathSciNet: MR2232725

Digital Object Identifier: 10.3150/bj/1151525129

Keywords: fractional Brownian motion , fractional integral , fractional Ornstein-Uhlenbeck process , fractional Vasicek model , Langevin equation , long-range dependence , Riemann-Stieltjes integrals , state space transform , stochastic calculus , Stochastic differential equations

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