Open Access
Translator Disclaimer
2007 Dynamical properties and characterization of gradient drift diffusions
Sébastien Darses, Ivan Nourdin
Author Affiliations +
Electron. Commun. Probab. 12: 390-400 (2007). DOI: 10.1214/ECP.v12-1324

Abstract

We study the dynamical properties of the Brownian diffusions having $\sigma\,{\rm Id}$ as diffusion coefficient matrix and $b=\nabla U$ as drift vector. We characterize this class through the equality $D^2_+=D^2_-$, where $D_{+}$ (resp. $D_-$) denotes the forward (resp. backward) stochastic derivative of Nelson's type. Our proof is based on a remarkable identity for $D_+^2-D_-^2$ and on the use of the martingale problem.

Citation

Download Citation

Sébastien Darses. Ivan Nourdin. "Dynamical properties and characterization of gradient drift diffusions." Electron. Commun. Probab. 12 390 - 400, 2007. https://doi.org/10.1214/ECP.v12-1324

Information

Accepted: 21 October 2007; Published: 2007
First available in Project Euclid: 6 June 2016

zbMATH: 1128.60065
MathSciNet: MR2350576
Digital Object Identifier: 10.1214/ECP.v12-1324

Subjects:
Primary: 60J60

JOURNAL ARTICLE
11 PAGES


SHARE
Back to Top