Fractional integral equations and state space transforms

Boris Buchmann; Claudia Klüppelberg

doi:10.3150/bj/1151525129

Fractional integral equations and state space transforms

Boris Buchmann^*, Claudia Klüppelberg

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

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.

Original language	English
Pages (from-to)	431-456
Number of pages	26
Journal	Bernoulli
Volume	12
Issue number	3
DOIs	https://doi.org/10.3150/bj/1151525129
Publication status	Published - Jun 2006

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title = "Fractional integral equations and state space transforms",

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 = "Fractional Brownian motion, Fractional Ornstein-Uhlenbeck process, Fractional Vasicek model, Fractional integral, Langevin equation, Long-range dependence, Riemann-Stieltjes integrals, Solution of stochastic differential equations, State space transform, Stochastic calculus",

author = "Boris Buchmann and Claudia Kl{\"u}ppelberg",

year = "2006",

month = jun,

doi = "10.3150/bj/1151525129",

language = "English",

volume = "12",

pages = "431--456",

journal = "Bernoulli",

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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 - https://www.scopus.com/pages/publications/33846108890

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 -

Fractional integral equations and state space transforms

Abstract

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