TY - JOUR
T1 - Fractional integral equations and state space transforms
AU - Buchmann, Boris
AU - Klüppelberg, Claudia
PY - 2006/6
Y1 - 2006/6
N2 - 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.
AB - 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.
KW - Fractional Brownian motion
KW - Fractional Ornstein-Uhlenbeck process
KW - Fractional Vasicek model
KW - Fractional integral
KW - Langevin equation
KW - Long-range dependence
KW - Riemann-Stieltjes integrals
KW - Solution of stochastic differential equations
KW - State space transform
KW - Stochastic calculus
UR - http://www.scopus.com/inward/record.url?scp=33846108890&partnerID=8YFLogxK
U2 - 10.3150/bj/1151525129
DO - 10.3150/bj/1151525129
M3 - Article
SN - 1350-7265
VL - 12
SP - 431
EP - 456
JO - Bernoulli
JF - Bernoulli
IS - 3
ER -