Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series

• Autorzy: M. Magdziarz , A. Weron
• Języki publikacji: EN

Abstrakty

EN

We introduce a fractional Langevin equation with α-stable noise and show that its solution ${Y_{κ}(t), t ≥ 0}$ is the stationary α-stable Ornstein-Uhlenbeck-type process recently studied by Taqqu and Wolpert. We examine the asymptotic dependence structure of $Y_{κ}(t)$ via the measure of its codependence r(θ₁,θ₂,t). We prove that $Y_{κ}(t)$ is not a long-memory process in the sense of r(θ₁,θ₂,t). However, we find two natural continuous-time analogues of fractional ARIMA time series with long memory in the framework of the Langevin equation.

Kategorie tematyczne

• 60G52: Stable processes
• 60G10: Stationary processes
• 60H10: Stochastic ordinary differential equations
• 62M10: Time series, auto-correlation, regression, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 181
• Numer: 1
• Strony: 47-60

Daty

wydano

2007

Twórcy

autor

M. Magdziarz

• Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wrocław University of Technology, 50-370 Wrocław, Poland

autor

A. Weron

• Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wrocław University of Technology, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm181-1-4