Averaged deviations of Orlicz processes and majorizing measures

Modern Stochastics: Theory and Applications

Rostyslav Yamnenko¹ 

[1] Taras Shevchenko National University of Kyiv, Ukraine;

关键词: Orlicz space;    Orlicz process;    supremum distribution;    method of majorizing measures;    Ornstein–Uhlenbeck process;   

DOI  :  10.15559/16-VMSTA64

来源: DOAJ

【 摘 要 】

This paper is devoted to investigation of supremum of averaged deviations $|X(t)-f(t)-\int _{\mathbb{T}}(X(u)-f(u))\hspace{0.1667em}\mathrm{d}\mu (u)/\mu (\mathbb{T})|$ of a stochastic process from Orlicz space of random variables using the method of majorizing measures. An estimate of distribution of supremum of deviations $|X(t)-f(t)|$ is derived. A special case of the $L_{q}$ space is considered. As an example, the obtained results are applied to stochastic processes from the $L_{2}$ space with known covariance functions.

【 授权许可】

Unknown