Dynamical properties and characterization of gradient drift diffusions
Ivan Nourdin (University Paris VI)
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.
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Pages: 390-400
Publication Date: October 21, 2007
DOI: 10.1214/ECP.v12-1324
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