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Dynamical properties and characterization of gradient drift diffusions

   
@article{ECP1324,
	author = {Sébastien Darses and Ivan Nourdin},
	title = {Dynamical properties and characterization of gradient drift diffusions},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {12},
	year = {2007},
	keywords = {Gradient drift diffusion;  Time reversal;  Nelson stochastic derivatives;  Kolmogorov theorem;  Reversible diffusion; Stationary diffusion;  Martingale problem},
	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.},
	pages = {no. 37, 390-400},
	issn = {1083-589X},
	doi = {10.1214/ECP.v12-1324},    
        url = {http://ecp.ejpecp.org/article/view/1324}}