Teoriya Veroyatnostei i ee Primeneniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

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

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
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; Theory Probab. Appl., 64:2 (2019), 209–228

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}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3943120}
\zmath{https://zbmath.org/?q=an:07099809}
\elib{https://elibrary.ru/item.asp?id=37298294}
\transl
\jour Theory Probab. Appl.
\yr 2019
\vol 64
\issue 2
\pages 209--228
\crossref{https://doi.org/10.1137/S0040585X97T989453}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000478971000003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071017499}


Linking options:
  • http://mi.mathnet.ru/eng/tvp5195
  • https://doi.org/10.4213/tvp5195
  • http://mi.mathnet.ru/eng/tvp/v64/i2/p258

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Теория вероятностей и ее применения Theory of Probability and its Applications
    Number of views:
    This page:169
    References:19
    First page:11

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021