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- W2791562034 abstract "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." @default.
- W2791562034 created "2018-03-29" @default.
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- W2791562034 date "2018-01-01" @default.
- W2791562034 modified "2023-09-25" @default.
- W2791562034 title "On relation between one multiple and a corresponding one-dimensional integral with applications" @default.
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- W2791562034 doi "https://doi.org/10.2298/yjor160916020b" @default.
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