## The Annals of Probability

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

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

Vlad Bally and Lucia Caramellino

#### Abstract

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

**Source**

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

**Dates**

Received: September 2014

Revised: December 2015

First available in Project Euclid: 15 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1494835223

**Digital Object Identifier**

doi:10.1214/16-AOP1092

**Mathematical Reviews number (MathSciNet)**

MR3650407

**Zentralblatt MATH identifier**

1371.60101

**Subjects**

Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus

Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

**Keywords**

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

#### Citation

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. https://projecteuclid.org/euclid.aop/1494835223