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- W1978392737 abstract "We consider the space C[0, 1] together with its Borel σ-algebra A and a Wiener measure P. Let Ω denote a point in C[0, 1] and let x(Ω, t) denote the coordinate process. Then, {x(Ω, t), tε[0, 1]} is a Wiener process, and stochastic integrals of the form $$intlimits_0^1 varphi {text{ }}(omega ,t)dx(omega ,t)$$ can be defined for a suitable class of ϕ. In this paper we consider a sequence of Stieltjes integrals of the form $$I_n = intlimits_0^1 varphi {text{ }}(omega ^n (omega ),t)dx(omega ^n (omega ),t)$$ where {Ω n (Ω)} is a sequence of polygonal approximations to co. Conditions are found which ensure the quadratic-mean convergence of {I n }, and the limit is expressed as the sum of the stochastic integral $$intlimits_0^1 varphi {text{ }}(omega ,t)dx(omega ,t)$$ and a “correction term”." @default.
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- W1978392737 date "1969-01-01" @default.
- W1978392737 modified "2023-09-24" @default.
- W1978392737 title "Riemann-Stieltjes approximations of stochastic integrals" @default.
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- W1978392737 doi "https://doi.org/10.1007/bf00531642" @default.
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