TY - JOUR
AU - BAJI´C, Tatjana
PY - 2017/08/14/
TI - On relation between one multiple and corresponding one-dimensional integral with applications
JF - Yugoslav Journal of Operations Research; Vol 28 No 1 (2018): Vol 28, No 1
KW -
N2 - 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.
UR - http://yujor.fon.bg.ac.rs/index.php/yujor/article/view?path=