Dynamical properties and characteriza-tion of gradient drift diffusion

Electronic Communications in Probability

Volumn 12, Issue , 2007, Pages 390-400

  Darses, Sébastien ^a   Nourdin, Ivan ^b  

^a Boston University   (United States)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Gradient drift diffusion; Kolmogorov theorem; Martingale problem; Nelson stochastic derivatives; Reversible diffusion; Stationary diffusion; Time reversal

Indexed keywords

EID: 35548995069     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: 10.1214/ECP.v12-1324     Document Type: Article

References (13)

1. J. Cresson and S. Darses (2006): Plongement stochastique des systèmes lagrangiens. C.R. Acad. Sci. Paris Ser. I 342, no. 5, 333-336.
2. S. Darses and I. Nourdin (2007): Stochastic derivatives for fractional diffusions. Ann. Probab 35, no. 5, 1998-2020.
3. H. Follmer (1984): Time reversal on Wiener space. Stochastic processes - mathematics and physics (Bielefeld). Lecture Notes in Math. 1158, 119-129.
4. I. Karatzas and S.E. Shreve (1991): Brownian Motion and Stochastic Calculus. Springer-Verlag, New York Second Edition.
5. A.N. Kolmogorov (1937): Zur Umkehrbarkeit der statistischen Naturgesetze. Math. Ann. 113, no. 1, 766-772.
6. A. Millet, D. Nualart and M. Sanz (1989): Integration by parts and time reversal for diffusion processes. Ann. Probab. 17, no. 1, 208-238.
7. E. Nelson (2001): Dynamical theory of Brownian motion. Princeton University Press. Second edition.
8. E. Pardoux (1986): Grossissement d’une filtration et retournement du temps d’une diffusion. Seminaire de Probabilites XX, 1984/85, 48-55, Lecture Notes in Math. 1204, Springer, Berlin.
9. L.C.G. Rogers and D. Williams (1987): Diffusions, Markov processes, and martingales. Vol. 2. Itô calculus. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley and Sons, Inc., New York. 475 pp.
10. S. Roelly and M. Thieullen (2005): Duality formula for the bridges of a Brownian diffusion: application to gradient drifts. Stochastic Process. Appl. 115, no. 10, 1677-1700.
11. G. Royer (1999): Une initiation aux inegalites de Sobolev logarithmiques. (French) [An introduction to logarithmic Sobolev inequalities] Cours Specialises [Specialized Courses], 5. Societe Mathematique de France, Paris, 114 pp.
12. M. Thieullen (1993): Second order stochastic differential equations and non-Gaussian reciprocal diffusions. Probab. Theory Related Fields 97, 231-257.
13. Zheng, W. A. and Meyer, P.-A. (1984): Quelques résultats de”mécanique stochastique”. (French) [Some results in”stochastic mechanics”] Seminaire de Probabilites XVIII, 223-244, Lecture Notes in Math., 1059, Springer, Berlin.