• Bernoulli
  • Volume 12, Number 3 (2006), 431-456.

Fractional integral equations and state space transforms

Boris Buchmann and Claudia Klüppelberg

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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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Bernoulli, Volume 12, Number 3 (2006), 431-456.

First available in Project Euclid: 28 June 2006

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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


Buchmann, Boris; Klüppelberg, Claudia. Fractional integral equations and state space transforms. Bernoulli 12 (2006), no. 3, 431--456. doi:10.3150/bj/1151525129.

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