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Fractional Integral Equations and State Space Transforms

Date

Authors

Buchmann, Boris

Klueppelberg, Claudia C

Publisher

Chapman & Hall

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.

Keywords

Keywords: Fractional Brownian motion; Fractional integral; Fractional Ornstein-Uhlenbeck process; Fractional Vasicek model; Langevin equation; Long-range dependence; Riemann-Stieltjes integrals; Solution of stochastic differential equations; State space transform;

URI

http://hdl.handle.net/1885/24366

Collections

ANU Research Publications

Source

Bernoulli

Type

Journal article

DOI

10.3150/bj/1151525129

Restricted until

2037-12-31

Downloads

File

Description

01_Buchmann_Fractional_Integral_Equations_2006.pdf (270.99 KB)

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