On relation between one multiple and a corresponding one-dimensional integral with applications

Yugoslav Journal of Operations Research

Bajić Tatjana¹ 

[1] Higher Education School of Professional Studies for Preschool Teachers, Šabac;

关键词: multiple stochastic integral;    multiple integral;    Gaussian quadrature rule;   

DOI  :  10.2298/YJOR160916020B

来源: DOAJ

【 摘 要 】

For a given finite positive measure on an interval I ⊆ R, a multiple stochastic integral of a Volterra kernel with respect to a product of a corresponding Gaussian orthogonal stochastic measure is introduced. The Volterra kernel is taken such that the multiple stochastic integral is a multiple iterated stochastic integral related to a parameterized Hermite polynomial, where parameter depends on Gaussian distribution of an underlying one-dimensional stochastic integral. Considering that there exists a connection between stochastic and deterministic integrals, we expose some properties of parameterized Hermite polynomials of Gaussian random variable in order to prove that one multiple integral can be expressed by a corresponding one-dimensional integral. Having in mind the obtained result, we show that a system of multiple integrals, as well as a collection of conditional expectations can be calculated exactly by generalized Gaussian quadrature rule.

【 授权许可】

Unknown