Integration by Parts, Homogeneous Chaos Expansions and Smooth Densities

Robert J. Elliott; Michael Kohlmann

doi:10.1214/aop/1176991504

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Home > Journals > Ann. Probab. > Volume 17 > Issue 1 > Article

January, 1989 Integration by Parts, Homogeneous Chaos Expansions and Smooth Densities

Robert J. Elliott, Michael Kohlmann

Ann. Probab. 17(1): 194-207 (January, 1989). DOI: 10.1214/aop/1176991504

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Abstract

By iterating a martingale representation result a homogeneous chaos expansion is obtained. Using the martingale representation, the integration-by-parts formula of the Malliavin calculus is derived using properties of stochastic flows. The infinite-dimensional calculus of variations is not required.

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Robert J. Elliott. Michael Kohlmann. "Integration by Parts, Homogeneous Chaos Expansions and Smooth Densities." Ann. Probab. 17 (1) 194 - 207, January, 1989. https://doi.org/10.1214/aop/1176991504

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Published: January, 1989

First available in Project Euclid: 19 April 2007

zbMATH: 0671.60050

MathSciNet: MR972781

Digital Object Identifier: 10.1214/aop/1176991504

Subjects:

Primary: 60H07

Secondary: 60H10 , 60J60

Keywords: homogeneous chaos , integration by parts , Malliavin calculus , Martingale representation , smooth densities , stochastic flow

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Ann. Probab.

Vol.17 • No. 1 • January, 1989

Institute of Mathematical Statistics

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Robert J. Elliott, Michael Kohlmann "Integration by Parts, Homogeneous Chaos Expansions and Smooth Densities," The Annals of Probability, Ann. Probab. 17(1), 194-207, (January, 1989)

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