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Dynamical properties and characterization of gradient drift diffusions


 
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1. Title Title of document Dynamical properties and characterization of gradient drift diffusions
 
2. Creator Author's name, affiliation, country Sébastien Darses; Boston University
 
2. Creator Author's name, affiliation, country Ivan Nourdin; University Paris VI
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Gradient drift diffusion; Time reversal; Nelson stochastic derivatives; Kolmogorov theorem; Reversible diffusion; Stationary diffusion; Martingale problem
 
3. Subject Subject classification 60J60
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2007-10-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1324
 
10. Identifier Digital Object Identifier 10.1214/ECP.v12-1324
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 12
 
12. Language English=en
 
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