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

M. Magdziarz, A. Weron (2007)

Studia Mathematica

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...

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