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

M. Magdziarz, and A. Weron. "Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series." Studia Mathematica 181.1 (2007): 47-60. <http://eudml.org/doc/285011>.

@article{M2007,
abstract = {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.},
author = {M. Magdziarz, A. Weron},
journal = {Studia Mathematica},
keywords = {long memory; fractional Langevin equation; -stable processes; Ornstein-Uhlenbeck process; fractional ARIMA time series},
language = {eng},
number = {1},
pages = {47-60},
title = {Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series},
url = {http://eudml.org/doc/285011},
volume = {181},
year = {2007},
}

TY - JOUR
AU - M. Magdziarz
AU - A. Weron
TI - Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series
JO - Studia Mathematica
PY - 2007
VL - 181
IS - 1
SP - 47
EP - 60
AB - 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.
LA - eng
KW - long memory; fractional Langevin equation; -stable processes; Ornstein-Uhlenbeck process; fractional ARIMA time series
UR - http://eudml.org/doc/285011
ER -