Fractional Langevin equation with $\alpha $-stable noise.
A link to fractional ARIMA time series
Studia Mathematica, Tome 181 (2007) no. 1, pp. 47-60
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We introduce a fractional Langevin equation with $\alpha$-stable noise
and show that its solution $\{ Y_\kappa(t),\, t\geq 0 \}$
is the stationary $\alpha$-stable Ornstein–Uhlenbeck-type process
recently studied by Taqqu and Wolpert.
We examine the asymptotic dependence structure of $Y_\kappa(t)$ via the measure of
its codependence $r(\theta_1,\theta_2,t)$. We prove that $Y_\kappa(t)$ is not a long-memory process
in the sense of $r(\theta_1,\theta_2,t)$. However, we find
two natural continuous-time analogues of fractional ARIMA time series with
long memory in the framework of the Langevin equation.
Keywords:
introduce fractional langevin equation alpha stable noise its solution kappa geq stationary alpha stable ornstein uhlenbeck type process recently studied taqqu wolpert examine asymptotic dependence structure kappa via measure its codependence theta theta prove kappa long memory process sense theta theta however natural continuous time analogues fractional arima time series long memory framework langevin equation
Affiliations des auteurs :
M. Magdziarz 1 ; A. Weron 1
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author = {M. Magdziarz and A. Weron},
title = {Fractional {Langevin} equation with $\alpha $-stable noise.
{A} link to fractional {ARIMA} time series},
journal = {Studia Mathematica},
pages = {47--60},
publisher = {mathdoc},
volume = {181},
number = {1},
year = {2007},
doi = {10.4064/sm181-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm181-1-4/}
}
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M. Magdziarz; A. Weron. Fractional Langevin equation with $\alpha $-stable noise. A link to fractional ARIMA time series. Studia Mathematica, Tome 181 (2007) no. 1, pp. 47-60. doi: 10.4064/sm181-1-4
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