Free Access
Issue
ESAIM: PS
Volume 7, March 2003
Page(s) 251 - 277
DOI https://doi.org/10.1051/ps:2003012
Published online 15 May 2003
  1. S. Albeverio, Yu.G. Kondratiev and M. Röckner, Analysis and geometry on configuration spaces: The Gibbsian case. J. Funct. Anal. 157 (1998) 242-291. [CrossRef] [MathSciNet]
  2. S. Albeverio, M. Röckner and T.S. Zhang, Markov uniqueness for a class of infinite dimensional Dirichlet operators. Stochastic Process. Optimal Control, Stochastics Monogr. 7 (1993) 1-26.
  3. P. Cattiaux, S. Rœlly and H. Zessin, Une approche gibbsienne des diffusions browniennes infini-dimensionnelles. Probab. Theory Related Fields 104-2 (1996) 223-248.
  4. P. Dai Pra, S. Rœlly and H. Zessin, A Gibbs variational principle in space-time for infinite-dimensional diffusions. Probab. Theory Related Fields 122 (2002) 289-315. [CrossRef] [MathSciNet]
  5. D. Dereudre, Une caractérisation de champs de Gibbs canoniques sur Formula et Formula . C. R. Acad. Sci. Paris Sér. I 335 (2002) 177-182.
  6. D. Dereudre, Diffusions infini-dimensionnelles et champs de Gibbs sur l'espace des trajectoires continues Formula . Thèse soutenue à l'École Polytechnique (2002).
  7. J.D. Deuschel, Infinite dimensionnal diffusion processes as Gibbs measures on Formula . Probab. Theory Related Fields 76 (1987) 325-340. [CrossRef] [MathSciNet]
  8. R.L. Dobrushin and J. Fritz, Non-equilibrium dynamics of one-dimensional infinite particle systems with a hard-core interaction. Comm. Math. Phys. 55 (1977) 275-292. [CrossRef] [MathSciNet]
  9. H. Föllmer, Time reversal on Wiener space. Springer-Verlag, Lecture Notes in Math. 1158 (1986) 117-129.
  10. H. Föllmer and A. Wakolbinger, Time reversal of infinite-dimensional diffusions. Stochastic Process. Appl. 22 (1986) 59-77. [CrossRef] [MathSciNet]
  11. M. Fradon, S. Roelly and H. Tanemura, An infinite system of Brownian balls with infinite range interaction. Stochastic Process. Appl. 90-1 (2000) 43-66. [CrossRef]
  12. J. Fritz, Gradient dynamics of infinite point systems. Ann. Probab. 15 (1987) 487-514.
  13. J. Fritz and R.L. Dobrushin, Non-equilibrium dynamics of two-dimensional infinite particle systems with a singular interaction. Comm. Math. Phys. 57 (1977) 67-81. [CrossRef] [MathSciNet]
  14. J. Fritz, S. Rœlly and H. Zessin, Stationary states of interacting Brownian motions. Stud. Sci. Math. Hung. 34 (1998) 151-164.
  15. B. Gaveau and P. Trauber, L'intégrale stochastique comme opérateur de divergence dans l'espace fonctionnel. J. Funct. Anal. 46 (1996) 230-238. [CrossRef]
  16. H.-O. Georgii, Canonical Gibbs measures. Springer, Lecture Notes in Math. 760 (1979).
  17. H.-O. Georgii, Equilibria for particle motions: Conditionally balanced point random fields, Exchangeability in Probability and Statistics, edited by Koch, Spizzichino. North Holland (1982) 265-280.
  18. E. Glötzl, Gibbsian description of point processes, in Colloquia Mathematica Societatis Janos Bolyai, 24 keszthely. Hungary (1978) 69-84.
  19. E. Glötzl, Lokale Energien und Potentiale für Punktprozesse. Math. Nach. 96 (1980) 195-206. [CrossRef]
  20. J. Jacod, Calcul stochastique et problèmes de matingales. Springer, Lecture Notes in Math. 714 (1979).
  21. R. Lang, Unendlich-dimensionale Wienerprozesse mit Wechselwirkung I. Z. Wahrsch. Verw. Gebiete 38 (1977) 55-72. [CrossRef]
  22. R. Lang, Unendlich-dimensionale Wienerprozesse mit Wechselwirkung II. Z. Wahrsch. Verw. Gebiete 39 (1977) 277-299. [CrossRef]
  23. K. Matthes, J. Kerstan and J. Mecke, Infinitely Divisible Point Process. J. Wiley (1978).
  24. A. Millet, D. Nualart and M. Sanz, Time Reversal for infinite-dimensional diffusions. Probab. Theory Related Fields 82 (1989) 315-347. [CrossRef] [MathSciNet]
  25. R.A. Minlos, S. Rœlly and H. Zessin, Gibbs states on space-time. Potential Anal. 13 (2000) 367-408. [CrossRef] [MathSciNet]
  26. X.X. Nguyen and H. Zessin, Integral and differential characterizations of the Gibbs process. Math. Nach. 88 (1979) 105-115. [CrossRef]
  27. C. Preston, Random fields. Springer, Lecture Notes in Math. 714 (1976).
  28. N. Privault, A characterization of grand canonical Gibbs measures by duality. Potential Anal. 15 (2001) 23-28. [CrossRef] [MathSciNet]
  29. B. Rauchenschwandtner and A. Wakolbinger, Some aspects of the Papangelou kernel, in Colloquia mathematica societatis Janos Bolyai, 24 keszthely. Hungary (1978) 325-336.
  30. S. Rœlly and H. Zessin, Une caractérisation de champs gibbsiens sur un espace de trajectoires. C. R. Acad. Sci. Paris Sér. I 321 (1995) 1377-1382.
  31. D. Ruelle, Statistical Mechanics. Rigorous Results.. Benjamin, New York (1969) .
  32. D. Ruelle, Superstable interactions in classical statistical mechanics. Comm. Math. Phys. 18 (1970) 127-159. [CrossRef] [MathSciNet]
  33. M. Yoshida, Construction of infinite dimensional interacting diffusion processes through Dirichlet forms. Probab. Theory Related Fields 106 (1996) 265-297. [CrossRef] [MathSciNet]