Champs markoviens et mesures de Gibbs sur R

N. Dang-Ngoc; M. Yor

Annales scientifiques de l'École Normale Supérieure (1978)

  • Volume: 11, Issue: 1, page 29-69
  • ISSN: 0012-9593

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Dang-Ngoc, N., and Yor, M.. "Champs markoviens et mesures de Gibbs sur ${R}$." Annales scientifiques de l'École Normale Supérieure 11.1 (1978): 29-69. <http://eudml.org/doc/82009>.

@article{Dang1978,
author = {Dang-Ngoc, N., Yor, M.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Convolution Semigroups; Markov Process; GibBs Probability Measures; QuasiInvariant Measures; Statistical Mechanics; Markov Fields; Positive Recurrent Semigroups},
language = {fre},
number = {1},
pages = {29-69},
publisher = {Elsevier},
title = {Champs markoviens et mesures de Gibbs sur $\{R\}$},
url = {http://eudml.org/doc/82009},
volume = {11},
year = {1978},
}

TY - JOUR
AU - Dang-Ngoc, N.
AU - Yor, M.
TI - Champs markoviens et mesures de Gibbs sur ${R}$
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1978
PB - Elsevier
VL - 11
IS - 1
SP - 29
EP - 69
LA - fre
KW - Convolution Semigroups; Markov Process; GibBs Probability Measures; QuasiInvariant Measures; Statistical Mechanics; Markov Fields; Positive Recurrent Semigroups
UR - http://eudml.org/doc/82009
ER -

References

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  1. [1] G. CHOQUET et J. DENY, Sur l'équation de convolution, µ = µ * σ (C. R. Acad. Sc., t. 250, série A, 1960, p. 799-801). Zbl0093.12802MR22 #9808
  2. [2] K. L. CHUNG, Some Universal Field Equations [Séminaire de Probabilités VI, p. 90-97 (Lecture Notes in Math., Springer)]. Zbl0238.60034MR51 #9175
  3. [3] Ph. COURRÈGE et P. RENOUARD, Oscillateur anharmonique, mesures quasi invariantes sur C (R, R) (Astérisque, Soc. Math. Fr., n° 22-23, 1975). Zbl0316.60009
  4. [4] N. DANG NGOC and G. ROYER, Markov Property of Extremal Local Fields [Proc. A.M.S., 1977 (à paraître)]. Zbl0406.60062
  5. [5] R. L. DOBRUSHIN, Description of a Random Field by Means of Conditionnal Probabilities and the Conditions Governing its Regularity (Theor. Probability Appl., vol. 13, 1968, p. 197-224). 
  6. [6] M. DUFLO et D. REVUZ, Propriétés asymptotiques des probabilités de transition des processus de Markov récurrents (Ann. Inst. Henri-Poincaré, vol. 5, 1969, p. 233-244). Zbl0183.47003MR42 #8557
  7. [7] E. B. DYNKIN, The Initial and Final Behavior of Trajectories of Markov Processes [Russ. Math. Surveys (Uspekhi), vol. 26, 1971, p. 165-182]. Zbl0281.60087MR45 #7807
  8. [8] H. FÖLLMER, Phase Transition and Martin Boundary [Séminaire de Probabilités IX (Lecture Notes in Math., 1975, Springer)]. Zbl0367.60112
  9. [9] H. FÖLLMER, On the Potential Theory of Stochastic Fields (Proceedings of International Statistical Institute, 40th Session, Warsaw, septembre 1975). Zbl0364.60114
  10. [10] F. GUERRA, L. ROSEN and B. SIMON, The P (φ)2 Euclidean Quantum Fields as Classical Statistical Mechanics (Ann. of Math., vol. 101, 1976, p. 111-259). MR51 #14836
  11. [11] T. E. HARRIS, The Existence of Stationary Measures for Certain Markov Processes (Proc. Third. Berkeley Symp. Math. Stat. Prob. II, 1956, p. 113-124). Zbl0072.35201MR18,941d
  12. [12] K. ICHIHARA and H. KUNITA, A Classification of the Second Order Degenerate Elliptic Operators and its Probabilistic Applications (Z. Wahrscheinlichkeitstheorie verw., Geb. 30, 1974, p. 235-254). Zbl0326.60097MR52 #1904
  13. [13] B. JAMISON and S. OREY, Markov Chains Recurrent in the Sense of Harris (Z. Wahrscheinlichkeitstheorie verw., Geb. 8, 1967, p. 41-48). Zbl0153.19802MR35 #6211
  14. [14] H. KESTEN, Existence and Uniqueness of Countable One-Dimensional Markov Random Fields (Ann. of Prob., vol. 4, 1976, p. 556-569). Zbl0367.60080MR53 #14671
  15. [15] F. KNIGHT, A Remark on Markovian Germ Fields (Z. Wahrscheinlichkeitstheorie, vol. 15, 1970, p. 291-296). Zbl0187.14703MR44 #7636
  16. [16] O. LANFORD and D. RUELLE, Observables at Infinity and States with short Range Correlations in Statistical Mechanics (Comm. Math. Phys., vol. 13, 1969, p. 194-215). MR41 #1343
  17. [17] V. MANDREKAR, Germ-field Markov Property for Multiparameter Processes [Séminaire de Probabilités X, p. 78-85 (Lecture Notes in Math., 1976, Springer)]. Zbl0332.60049MR55 #13555
  18. [18] P. A. MEYER et M. YOR, Sur la théorie de la prédiction et le problème de décomposition des tribus F0t+ [Séminaire de Probabilités X, p. 104-117 (Lecture Notes in Math., 1976, Springer)]. Zbl0332.60025
  19. [19] E. NELSON, Construction of Quantum Fields from Markov Fields (J. Funct. Anal., vol. 12, 1973, p. 97-112). Zbl0252.60053MR49 #8555
  20. [20] E. NELSON, Dynamical Theories of Brownian Motion (Mathematical Notes, Princeton University Press). Zbl0165.58502
  21. [21] J. NEVEU, Base mathématique du calcul des probabilités, Masson, Paris, 1970. Zbl0203.49901MR42 #6885
  22. [22] C. J. PRESTON, Gibbs States on Countable Sets, Cambridge University Press, London-New York, 1974. Zbl0297.60054MR57 #14194a
  23. [23] P. PRIOURET et M. YOR, Processus de diffusion et mesures quasi invariantes sur C (R, R) (Astérisque, Soc. Math. Fr., n° 22-23, 1975). Zbl0316.60051MR58 #14757
  24. [24] D. REVUZ, Markov Chains, North Holland Mathematical Library, 1975. Zbl0332.60045MR54 #3852
  25. [25] G. ROYER, Unicité de certaines mesures quasi invariantes sur C (R) (Ann. scient. Éc. Norm. Sup., t. 8, 1975, p. 319-338). Zbl0351.60004MR52 #10987
  26. [26] G. ROYER et M. YOR, Représentation intégrale de certaines mesures quasi invariantes sur C (R) ; mesures extrémales et propriété de Markov (Ann. Inst. Fourier, vol. 26, 1976, p. 7-24). Zbl0295.28025MR56 #5828
  27. [27] D. RUELLE, Statistical Mechanics, Benjamin, New York, 1969. Zbl0177.57301MR44 #6279
  28. [28] F. SPITZER, Phase Transition in One-Dimensional Nearest Neighbor Systems (J. Funct. Anal., vol. 20, 1975, p. 240-254). Zbl0333.60063MR52 #9419
  29. [29] J. T. COX, Entrance Laws for Markov Chains (Annals of Prob., vol. 5, 1977, p. 533-549). Zbl0369.60079MR56 #13368
  30. [30] E. B. DYNKIN and J. E. KUZNECOV, Determining Functions of Markov Processes (Dokl. Akad. Nauk., vol. 214, 1974, English Transl., vol. 15, 1974, p. 20-23). Zbl0334.60032

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