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February, 1977 Wiener Functionals as Ito Integrals
R. M. Dudley
Ann. Probab. 5(1): 140-141 (February, 1977). DOI: 10.1214/aop/1176995898


Every measurable real-valued function $f$ on the space of Wiener process paths $\{W(t): 0 \leqq t \leqq 1\}$ can be represented as an Ito stochastic integral $\int^1_0 \varphi(t, \omega) dW(t, \omega)$ where $\varphi$ is a nonanticipating functional with $\int^1_0 \varphi(t, \omega)^2dt < \infty$ for almost all $\omega$.


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R. M. Dudley. "Wiener Functionals as Ito Integrals." Ann. Probab. 5 (1) 140 - 141, February, 1977.


Published: February, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0359.60071
MathSciNet: MR426151
Digital Object Identifier: 10.1214/aop/1176995898

Primary: 60H05
Secondary: 60G15 , 60G17 , 60G40 , 60J65

Keywords: stochastic integral , Wiener process

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • February, 1977
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