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On Relation Between One Multiple and a Corresponding One-Dimensional Integral With Applications
Yugoslav journal of operations research, Tome 28 (2018) no. 1, p. 79 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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For a given finite positive measure on an interval $I \subseteq \R$, 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.
Classification : 60H05, 60H30, 65R10, 65D32
Keywords: Multiple Stochastic Integral, Multiple Integral, Gaussian Quadrature Rule 
@article{YJOR_2018_28_1_a4,
     author = {Tatjana Baji\'c},
     title = {On {Relation} {Between} {One} {Multiple} and a {Corresponding} {One-Dimensional} {Integral} {With} {Applications}},
     journal = {Yugoslav journal of operations research},
     pages = {79 },
     year = {2018},
     volume = {28},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/YJOR_2018_28_1_a4/}
}
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Tatjana Bajić. On Relation Between One Multiple and a Corresponding One-Dimensional Integral With Applications. Yugoslav journal of operations research, Tome 28 (2018) no. 1, p. 79 . http://geodesic.mathdoc.fr/item/YJOR_2018_28_1_a4/