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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 that serve as almost sure asymptotic upper bounds for a displacement process given by an integrated time-varying Ornstein–Uhlenbeck process. The form of upper functions depends on the characteristics (the stability rate and the diffusion coefficient) of a stochastic linear differential equation. We introduce the notion of anomalous diffusion related to behavior of upper functions and compare the results of diffusion classification (normal diffusion, subdiffusion, and superdiffusion) with those obtained on the basis of mean square displacements.

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

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 5-100 This research was funded by the Russian Academic Excellence Project “5-100.”

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

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English version:
Theory of Probability and its Applications, 2019, 64:2, 209–228

Bibliographic databases:

PACS: 02.50.Ey 02.50.Fz
MSC: 60J60 65C30
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; Theory Probab. Appl., 64:2 (2019), 209–228

Citation in format AMSBIB
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