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Avtomat. i Telemekh., 2018, Issue 2, Pages 109–121 (Mi at15018)  

This article is cited in 2 scientific papers (total in 2 papers)

Stochastic Systems

An analytic study of the Ornstein–Uhlenbeck process with time-varying coefficients in the modeling of anomalous diffusions

E. S. Palamarchukab

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

Abstract: We consider the problem of modeling anomalous diffusions with the Ornstein–Uhlenbeck process with time-varying coefficients. An anomalous diffusion is defined as a process whose mean-squared displacement non-linearly grows in time which is nonlinearly growing in time. We classify diffusions into types (subdiffusion, normal diffusion, or superdiffusion) depending on the parameters of the underlying process. We solve the problem of finding the coefficients of dynamics equations for the Ornstein–Uhlenbeck process to reproduce a given mean-squared displacement function.

Keywords: process Ornstein–Uhlenbeck process, anomalous diffusion, Riccati equation, filtering, linear controller.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 5-100
The study has been funded by the Russian Academic Excellence Project “5-100”.


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English version:
Automation and Remote Control, 2018, 79:2, 289–299

Bibliographic databases:

Presented by the member of Editorial Board: Б. М. Миллер

Received: 08.04.2017

Citation: E. S. Palamarchuk, “An analytic study of the Ornstein–Uhlenbeck process with time-varying coefficients in the modeling of anomalous diffusions”, Avtomat. i Telemekh., 2018, no. 2, 109–121; Autom. Remote Control, 79:2 (2018), 289–299

Citation in format AMSBIB
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\by E.~S.~Palamarchuk
\paper An analytic study of the Ornstein--Uhlenbeck process with time-varying coefficients in the modeling of anomalous diffusions
\jour Avtomat. i Telemekh.
\yr 2018
\issue 2
\pages 109--121
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\zmath{https://zbmath.org/?q=an:1391.93200}
\elib{http://elibrary.ru/item.asp?id=32606206}
\transl
\jour Autom. Remote Control
\yr 2018
\vol 79
\issue 2
\pages 289--299
\crossref{https://doi.org/10.1134/S000511791802008X}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. S. Palamarchuk, “O verkhnikh funktsiyakh dlya anomalnykh diffuzii, modeliruemykh protsessom Ornshteina–Ulenbeka s peremennymi koeffitsientami”, Teoriya veroyatn. i ee primen., 64:2 (2019), 258–282  mathnet  crossref  elib
    2. Das A., Levina A., “Critical Neuronal Models With Relaxed Timescale Separation”, Phys. Rev. X, 9:2 (2019), 021062  crossref  isi
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