Fractional integral equations and state space transforms

Boris Buchmann, Claudia Klüppelberg

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

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 languageEnglish
Pages (from-to)431-456
Number of pages26
JournalBernoulli
Volume12
Issue number3
DOIs
StatePublished - Jun 2006

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

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