The Annals of Probability

On an Independence Criterion for Multiple Wiener Integrals

Olav Kallenberg

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Abstract

Ustunel and Zakai have recently obtained a necessary and sufficient condition for two multiple Wiener integrals with respect to the same Brownian motion to be independent. In the present note, the sufficiency of their condition is shown to be a simple consequence of the classical relationship between multiple Wiener integrals and Hermite polynomials. The original proofs use Malliavin calculus.

Article information

Source
Ann. Probab., Volume 19, Number 2 (1991), 483-485.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990436

Digital Object Identifier
doi:10.1214/aop/1176990436

Mathematical Reviews number (MathSciNet)
MR1106271

Zentralblatt MATH identifier
0738.60052

JSTOR
links.jstor.org

Subjects
Primary: 60H05: Stochastic integrals
Secondary: 60J65: Brownian motion [See also 58J65]

Keywords
Multiple Wiener integrals Hermite polynomials orthogonal expansions

Citation

Kallenberg, Olav. On an Independence Criterion for Multiple Wiener Integrals. Ann. Probab. 19 (1991), no. 2, 483--485. doi:10.1214/aop/1176990436. https://projecteuclid.org/euclid.aop/1176990436


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