Averaged deviations of Orlicz processes and majorizing measures

Rostyslav Yamnenko


This paper is devoted to investigation of supremum of averaged deviations $| X(t) - f(t) - \int_{\mathbb{T}} (X(u) - f(u)) \,\mathrm{d}\mu(u) / \mu(\mathbb{T})|$ 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.


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

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DOI: http://dx.doi.org/10.15559/16-VMSTA64


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