Short Communications

Uniform convergence of sub-gaussian integrals

A. A. Pashko

National Taras Shevchenko University of Kyiv

Abstract: This paper studies conditions and estimates of the uniform convergence in probability of strictly sub-Gaussian integrals
$$ S_a^b(t)=\int_a^bT(t,\lambda) d\xi(\lambda). $$
The estimate obtained coincides in order with analogous estimates for Gaussian integrals.

Keywords: stochastic integral, sub-Gaussian process, uniform convergence, estimate of convergence, condition of convergence.

Received: 02.08.1993
Revised: 20.04.1998

DOI: 10.4213/tvp2169

 English version: Theory of Probability and its Applications, 1999, 43:4, 650–655

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