Fractional integral equations and state space transforms

Buchmann, B.; Klüppelberg, C.

mediaTUM GesamtbestandEinrichtungenFakultätenFakultät für MathematikZentrum MathematikArbeitsgruppe Mathematische StatistikMathematische Statistik (Prof. Drton)Arbeitsgruppe Prof. KlüppelbergSST050322.pdf

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Document type:

Zeitschriftenaufsatz

Author(s):

Buchmann, B. and Klüppelberg, C.

Title:

Fractional integral equations and state space transforms

Abstract:

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

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, solution of SDE

Journal title:

Bernoulli

Year:

2006

Journal volume:

Journal issue:

Pages contribution:

431-456

Reviewed:

Language:

WWW:

https://projecteuclid.org/euclid.bj/1151525129