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• W775835849 abstract "Fix an integer m ≥ 1. Consider a measurable stochastic process I m which has a representation in terms of m-th multiple Wiener-Ito integrals I m(ht), t ∈ T, of a time dependent kernel h. Namely, let I m = {I m(h t);t ∈ T} with $$I_m(h_t)=int cdots int h_t(x_1,cdots,x_m)G(dx_1)cdots G(dx_m),;;;;;t in T,$$where h = h t = {h(t, ·); t ∈ T} is a family of square summable functions defined on the product measure space (X m, v m) and G is a Gaussian random measure with the control measure v. The problem we study in this paper is as follows: given a measurable function h on T × X m and given a Banach function space F(T, μ) of measurable functions on a separable σ-finite measure space (T,μ), when does $$I_m in F(T,mu);;;;;;almost;surely(a.s.)?;;;;;;;(1.1)$$If m = 1 then I 1 is a Gaussian process with the covariance function $$Ttimes T ni (t,s) mapsto int_X h_t(x) h_s(x)nu (dx)$$." @default.
• W775835849 created "2016-06-24" @default.
• W775835849 creator A5020619686 @default.
• W775835849 date "1994-01-01" @default.
• W775835849 modified "2023-10-18" @default.
• W775835849 title "Multiple Wiener-ITÔ Integral Processes with Sample Paths in Banach Function Spaces" @default.
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• W775835849 doi "https://doi.org/10.1007/978-1-4612-0253-0_22" @default.
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