The Annals of Probability

Regularity of Wiener functionals under a Hörmander type condition of order one

Vlad Bally and Lucia Caramellino

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We study the local existence and regularity of the density of the law of a functional on the Wiener space which satisfies a criterion that generalizes the Hörmander condition of order one (i.e., involving the first-order Lie brackets) for diffusion processes.

Article information

Ann. Probab., Volume 45, Number 3 (2017), 1488-1511.

Received: September 2014
Revised: December 2015
First available in Project Euclid: 15 May 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

Malliavin calculus local integration by parts formulas total variation distance variance of the Brownian path


Bally, Vlad; Caramellino, Lucia. Regularity of Wiener functionals under a Hörmander type condition of order one. Ann. Probab. 45 (2017), no. 3, 1488--1511. doi:10.1214/16-AOP1092.

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