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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


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.


Published: January, 1989
First available in Project Euclid: 19 April 2007

zbMATH: 0671.60050
MathSciNet: MR972781
Digital Object Identifier: 10.1214/aop/1176991504

Primary: 60H07
Secondary: 60H10 , 60J60

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

Rights: Copyright © 1989 Institute of Mathematical Statistics

Vol.17 • No. 1 • January, 1989
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