On the uniform convergence of stochastic integrals with respect to the norm of the Orlicz space. (Russian) Zbl 0577.60057

Kozachenko, Yu. V.

Teor. Veroyatn. Mat. Stat. 29, 52-64 (1983).

The author considers stochastic integrals of the form C(t)\(\int^{\infty}_{0}f(t,\lambda)dx(\lambda)\), where C and f are functions of exponential type, and x is a random process belonging to the Orlicz space of random variables, which is generated by the so called Orlicz function. Conditions for the uniform convergence of these integrals with respect to the Luxemburg norm and estimates for the probability, that the supremum of the integral does not exceed a certain level are obtained. These results are applied to the case, where x is Gaussian.

Reviewer: C.Baldauf

MSC:

60H05	Stochastic integrals
60E15	Inequalities; stochastic orderings
60B05	Probability measures on topological spaces

Keywords:

Orlicz space of random variables; Luxemburg norm; supremum of the integral