The Annals of Probability

On Independence and Conditioning On Wiener Space

Ali Suleyman Ustunel and Moshe Zakai

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Abstract

Let $I_p(f)$ and $I_q(g)$ be multiple Wiener-Ito integrals of order $p$ and $q$, respectively. A characterization of independence of general random variables on Wiener space in the context of the stochastic calculus of variations is derived and a necessary and sufficient condition on the pair of kernels $(f, g)$ is derived under which the random variables $I_p(f), I_q(g)$ are independent.

Article information

Source
Ann. Probab. Volume 17, Number 4 (1989), 1441-1453.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176991164

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176991164

Mathematical Reviews number (MathSciNet)
MR1048936

Zentralblatt MATH identifier
0693.60046

Subjects
Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60H05: Stochastic integrals 60J65: Brownian motion [See also 58J65]

Keywords
Independence Wiener chaos multiple Wiener-Ito integrals the Malliavin calculus

Citation

Ustunel, Ali Suleyman; Zakai, Moshe. On Independence and Conditioning On Wiener Space. Ann. Probab. 17 (1989), no. 4, 1441--1453. doi:10.1214/aop/1176991164. http://projecteuclid.org/euclid.aop/1176991164.


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