Minimization of the Kullback information of diffusion processes
Patrick Cattiaux; Christian Léonard
Annales de l'I.H.P. Probabilités et statistiques (1994)
- Volume: 30, Issue: 1, page 83-132
- ISSN: 0246-0203
Access Full Article
topHow to cite
topCattiaux, Patrick, and Léonard, Christian. "Minimization of the Kullback information of diffusion processes." Annales de l'I.H.P. Probabilités et statistiques 30.1 (1994): 83-132. <http://eudml.org/doc/77476>.
@article{Cattiaux1994,
author = {Cattiaux, Patrick, Léonard, Christian},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {relative entropy; Föllmer measure; Girsanov transformation; Kullback information; large deviations; measure valued empirical process; conservative diffusions},
language = {eng},
number = {1},
pages = {83-132},
publisher = {Gauthier-Villars},
title = {Minimization of the Kullback information of diffusion processes},
url = {http://eudml.org/doc/77476},
volume = {30},
year = {1994},
}
TY - JOUR
AU - Cattiaux, Patrick
AU - Léonard, Christian
TI - Minimization of the Kullback information of diffusion processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1994
PB - Gauthier-Villars
VL - 30
IS - 1
SP - 83
EP - 132
LA - eng
KW - relative entropy; Föllmer measure; Girsanov transformation; Kullback information; large deviations; measure valued empirical process; conservative diffusions
UR - http://eudml.org/doc/77476
ER -
References
top- [AN] R. Aebi and M. Nagasawa, Large Deviations and the Propagation of Chaos for Schrödinger Processes, Prob. Th. and Rel. Fields, Vol. 94, 1992, pp. 53- 68. Zbl0767.60056MR1189085
- [Bi] P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. Zbl0172.21201MR233396
- [Bru] M. Brunaud, Thèse, Université Paris-XI, 1989.
- [Ca] E. Carlen, Conservative Diffusions, Comm. Math. Phys., Vol. 94, 1984, pp. 293-316. Zbl0558.60059MR763381
- [Cx] P. Cattiaux, Calcul stochastique et opérateurs dégénérés du second ordre, part II, Problème de Dirichlet, Bull. Sc. Math., Vol. 115, 1991, pp. 81-122. Zbl0790.60048MR1086940
- [CL1] P. Cattiaux and C. Léonard, Minimization of the Kullback Information for Some Markov Processes (in preparation). Zbl0863.60073
- [CL2] P. Cattiaux, C. Léonard, Large Deviations and Nelson Processes, Preprint, 1992. Zbl0817.60021MR1307957
- [CP] P. Cattiaux and F. Petit, Nelson Processes Revisited (in preparation).
- [Cs] I. Csiszar, I-Divergence Geometry of Probability Distributions and Minimization Problems, Ann. of Prob., Vol. 3, 1984, pp. 146-158. Zbl0318.60013MR365798
- [DaG] D. Dawson and J. Gärtner, Large Deviations from the MacKean Vlasov Limit for Weakly Interacting Diffusions, Stochastics, Vol. 20, 1987, pp. 247- 308. Zbl0613.60021MR885876
- [DM4] C. Dellacherie and P.A. Meyer, Probabilités et potentiel, chp. XII-XVI, Hermann, 1987. MR488194
- [DS] J.D. Deuschel and D.W. Stroock, Large deviations, Academic Press, 1989. Zbl0705.60029MR997938
- [DS1] J.D. Deuschel and D.W. Stroock, A Function Space Large Deviation Principle for Certain Stochastic Integrals, Probab. Th. Rel. Fields, Vol. 83, 1989, pp. 279-307. Zbl0682.60018MR1012502
- [Fö] H. Föllmer, The Exit Measure of a Supermartingale, Z. W., Vol. 21, 1972, pp. 154-166. Zbl0231.60033MR309184
- [Fö1] H. Föllmer, Random Fields and Diffusion Processes, École d'été de Probabilités de St Flour, L.N. Math., Vol. 1362, 1988, pp. 101-204. Zbl0661.60063MR983373
- [Fö2] H. Föllmer, An Entropy Approach to the Time Reversal of Diffusion Processes, Proc. 4th IFIP Workshop on Stoch. Diff. Eq., M. MÉTIVIER and E. PARDOUX Ed., L.N. in Control and Information, 1987.
- [IW] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland, 1981. Zbl0495.60005MR637061
- [Jac] J. Jacod, Problèmes de martingales, L.N. Math., 714, 1979, Springer. Zbl0414.60053MR542115
- [Ku] H. Kunita, Stochastic Differential Equations and Stochastic Flows..., École d'été de Probabilités de St Flour, L.N. Math., Vol. 907, 1984, pp. 144-305.
- [Léo] C. Léonard, Thèse d'État, Université Paris-XI, 1991.
- [MZ1] P.A. Meyer and W.A. Zheng, Construction de processus de Nelson réversibles, Sem. Probab. XIX, L.N. Math., 1123, 1985, pp. 12-26. Zbl0564.60075MR889465
- [MZ2] P.A. Meyer and W.A. Zheng, Tightness Criteria for Laws of Semimartingales, Ann. I.H.P., Vol. 20, 1984, pp. 353-372. Zbl0551.60046MR771895
- [Mi] T. Mikami, P.H.D. Thesis, Brown University.
- [Na] M. Nagasawa, Schrödinger Equations and Diffusion Theory (to appear). Zbl0780.60003MR1227100
- [Ne] E. Nelson, Stochastic Mechanics and Random Fields, École d'été de Probabilités de St Flour, L.N. Math., 1362, 1988, pp. 429-450. Zbl0669.60097MR983376
- [Pe] F. Petit, Thèse, Université Paris-VII, 1991.
- [RZ] S. Roelly and H. Zessin, Sur la mécanique statistique d'une particule Browniennne sur le tore, Preprint, 1991.
- [Sha] M.J. Sharpe, General Theory of Markov Processes, Academic Press, 1988. Zbl0649.60079MR958914
- [SV] D.W. Stroock and S.R.S. Varadhan, On Degenerate Elliptic Parabolic Operators..., Comm. Pure. Appl. Math., Vol. 25, 1972, pp. 651-713. Zbl0344.35041MR387812
- [Ta] H. Tanabe, Equations of Evolution, Pitman1979. Zbl0417.35003MR533824
- [Zhe] W.A. Zheng, Tightness Results for Law of diffusion Processes, Application to Stochastic Mechanis, Ann. I.H.P., Vol. 21, 1985, pp. 103-124. Zbl0579.60050MR798890
Citations in EuDML Documents
top- Vladimir I. Bogachev, Nicolai V. Krylov, Michael Röckner, Elliptic regularity and essential self-adjointness of Dirichlet operators on
- Liming Wu, Quelques problèmes associés au processus de Donsker-Varadhan
- Christian Léonard, Large deviations for long range interacting particle systems with jumps
- E. Pardoux, R. J. Williams, Symmetric reflected diffusions
- Patrick Cattiaux, Christian Léonard, Minimization of the Kullback information for some Markov processes
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.