%A BAJI´C, Tatjana
%D 2017
%T On relation between one multiple and corresponding one-dimensional integral with applications
%B 2017
%9
%! On relation between one multiple and corresponding one-dimensional integral with applications
%K
%X For a given
finite positive measure on an interval I R , we introduce a multiple stochastic integral of a Volterra kernel with respect to a product of a corresponding Gaussian orthogonal stochastic measure. Indicating that the previous defi
ned multiple stochastic integral is in relation with a parameterized Hermite polynomial of a suitable stochastic integral, that is, of a suitable Gaussian random variable, we prove that one multiple integral can be expressed by a corresponding one-dimensional. Having in mind the obtained result, we show that a collection of the multiple integrals can be integrated exactly by a Gaussian quadrature rule. In particular, under certain conditions, a classical Gaussian quadrature rule can be used to approximate the value of one type of the multiple integral. A probabilistic interpretation is given. Keywords: Multiple stochastic integral, Multiple integral, Gaussian quadrature rule.
%U http://yujor.fon.bg.ac.rs/index.php/yujor/article/view?path=
%J Yugoslav Journal of Operations Research
%0 Journal Article
%V 28
%N 1
%@ 2334-6043
%8 2017-08-14
%7 2018-02-08