E. S. Palamarchuk, “On upper functions for anomalous diffusions governed by time-varying Ornstein–Uhlenbeck process”, Teor. Veroyatnost. i Primenen., 2019, Volume 64, Issue 2,Pages <nobr>258

This article is cited in 2 papers

On upper functions for anomalous diffusions governed by time-varying Ornstein–Uhlenbeck process

E. S. Palamarchuk^ab

^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.

PACS: 02.50.Ey 02.50.Fz

MSC: 60J60 65C30

Received: 18.04.2018
Revised: 01.09.2018
Accepted: 13.09.2018

DOI: 10.4213/tvp5195