Year: 2007
Type: article
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.
DOI: 10.1214/ecp.v12-1324
Authors: Sébastien Darses, Ivan Nourdin
Institutions: Boston University, Université Pierre-et-Marie-Curie
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W2083650671