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.
Publié le : 2006-06-14
Classification:
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
@article{1151525129,
author = {Buchmann, Boris and Kl\"uppelberg, Claudia},
title = {Fractional integral equations and state space transforms},
journal = {Bernoulli},
volume = {12},
number = {2},
year = {2006},
pages = { 431-456},
language = {en},
url = {http://dml.mathdoc.fr/item/1151525129}
}
Buchmann, Boris; Klüppelberg, Claudia. Fractional integral equations and state space transforms. Bernoulli, Tome 12 (2006) no. 2, pp. 431-456. http://gdmltest.u-ga.fr/item/1151525129/