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, Issue 2,Pages <nobr>109

This article is cited in 6 papers

Stochastic Systems

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

E. S. Palamarchuk^ab

^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.

Presented by the member of Editorial Board: B. M. Miller

Received: 08.04.2017