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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 2, Pages 258–282
DOI: https://doi.org/10.4213/tvp5195 (Mi tvp5195) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
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DOI: https://doi.org/10.4213/tvp5195
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.”
Received: 18.04.2018
Revised: 01.09.2018
Accepted: 13.09.2018
English version:
Theory of Probability and its Applications, 2019, Volume 64, Issue 2, Pages 209–228
DOI: https://doi.org/10.1137/S0040585X97T989453
Bibliographic databases:
Document Type: Article
PACS: 02.50.Ey 02.50.Fz
MSC: 60J60 65C30
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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