ON UPPER FUNCTIONS FOR ANOMALOUS DIFFUSIONS GOVERNED BY TIME-VARYING ORNSTEIN-UHLENBECK PROCESS

被引：3

作者：

Palamarchuk, E. S. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Cent Econ & Math Inst, Moscow, Russia

[2] Natl Res Univ Higher Sch Econ, Moscow, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2019年 / 64卷 / 02期

关键词：

time-varying Ornstein-Uhlenbeck process; upper function; anomalous diffusion; the law of the iterated logarithm; STOCHASTIC DIFFERENTIAL-EQUATION; OPTIMALITY;

D O I：

10.1137/S0040585X97T989453

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：209 / 228

页数：20

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