Theory of Probability and Mathematical Statistics
Fractional Stokes-Boussinesq-Langevin equation and Mittag-Leffler correlation decay
V. V. Anh, N. N. Leonenko
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Abstract: This paper presents some stationary processes which are solutions of the fractional Stokes-Boussinesq-Langevin equation. These processes have reflection positivity and their correlation functions, which may exhibit the Alder-Wainwright effect or long-range dependence, are expressed in terms of the Mittag-Leffler functions. These properties are established rigorously via the theory of KMO-Langevin equation and a combination of Mittag-Leffler functions and fractional derivatives. A~relationship to fractional Riesz-Bessel motion is also investigated. This relationship permits to study the effects of long-range dependence and second-order intermittency simultaneously.
Keywords: Anomalous diffusion, Stokes-Boussinesq-Langevin equation, Langevin equation with delay, long-range dependence, Mittag-Leffler function.
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