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Teor. Veroyatnost. i Primenen., 2019, Volume 64, Issue 2, Pages 258–282 (Mi tvp5195)  

On upper functions for anomalous diffusions governed by time-varying Ornstein–Uhlenbeck process

E. S. Palamarchukab

a Central Economics and Mathematics Institute Russian Academy of Sciences, Moscow
b National Research University "Higher School of Economics", Moscow

Abstract: We obtain upper functions which serve as almost sure asymptotic upper bounds for a displacement process given by integrated time-varying Ornstein-Uhlenbeck process. Derived upper functions depend on the stability rate and diffusion coefficient of the underlying linear stochastic differential equation. We introduce the notion of anomalous diffusion related to behavior of upper functions and compare the diffusion classification results (normal diffusion, sub-diffusion and super-diffusion) with those obtained from approach based on mean-squared displacement.

Keywords: time-varying Ornstein-Uhlenbeck process, upper function, anomalous diffusion, law of iterated logarithm

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 5-100


DOI: https://doi.org/10.4213/tvp5195

Full text: PDF file (575 kB)
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References: PDF file   HTML file

PACS: 02.50.Ey 02.50.Fz
MSC: 60J60 65C30
Received: 18.04.2018
Revised: 01.09.2018
Accepted:13.09.2018

Citation: E. S. Palamarchuk, “On upper functions for anomalous diffusions governed by time-varying Ornstein–Uhlenbeck process”, Teor. Veroyatnost. i Primenen., 64:2 (2019), 258–282

Citation in format AMSBIB
\Bibitem{Pal19}
\by E.~S.~Palamarchuk
\paper On upper functions for anomalous diffusions governed by time-varying Ornstein--Uhlenbeck process
\jour Teor. Veroyatnost. i Primenen.
\yr 2019
\vol 64
\issue 2
\pages 258--282
\mathnet{http://mi.mathnet.ru/tvp5195}
\crossref{https://doi.org/10.4213/tvp5195}
\elib{http://elibrary.ru/item.asp?id=37298294}


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