Fractional Stokes–Boussinesq–Langevin equation and Mittag-Leffler correlation decay

Anh, V.; Leonenko, N.

doi:10.1090/tpms/1060

Fractional Stokes–Boussinesq–Langevin equation and Mittag-Leffler correlation decay

Authors: V. V. Anh and N. N. Leonenko
Journal: Theor. Probability and Math. Statist. 98 (2019), 5-26
MSC (2010): Primary 60G10; Secondary 82C31
DOI: https://doi.org/10.1090/tpms/1060
Published electronically: August 19, 2019
MathSciNet review: 3824676
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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 the 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 us to study the effects of long-range dependence and second-order intermittency simultaneously.

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