Markov property of extremal local fields
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- by N. Dang-Ngoc and G. Royer PDF
- Proc. Amer. Math. Soc. 70 (1978), 185-188 Request permission
Abstract:
We show that extremal local field on ${(E,\mathcal {E})^T}$, with $T = {\mathbf {Z}}$ or R and $(E,\mathcal {E})$ standard, possesses the Markov property. This result generalizes that of F. Spitzer in the case $T = {\mathbf {Z}}$, E countable and a result of G. Royer and M. Yor on extremal measures associated to certain diffusion processes.References
- N. Dang Ngoc and M. Yor, Champs markoviens et mesures de Gibbs sur $\textbf {R}$, Ann. Sci. École Norm. Sup. (4) 11 (1978), no. 1, 29–69 (French, with English summary). MR 504421 H. Föllmer, Phase transition and Martin boundary, Séminaire Probabilités Strasbourg IX, Lecture Notes in Math., Springer-Verlag, Berlin and New York, 1976.
- Jacques Neveu, Bases mathématiques du calcul des probabilités, Masson et Cie, Éditeurs, Paris, 1970 (French). Préface de R. Fortet; Deuxième édition, revue et corrigée. MR 0272004
- G. Royer and M. Yor, Représentation intégrale de certaines mesures quasi-invariantes sur ${\cal C}(R)$; mesures extrémales et propriété de Markov, Ann. Inst. Fourier (Grenoble) 26 (1976), no. 2, ix, 7–24 (French, with English summary). MR 447517
- Frank Spitzer, Phase transition in one-dimensional nearest-neighbor systems, J. Functional Analysis 20 (1975), no. 3, 240–255. MR 0388583, DOI 10.1016/0022-1236(75)90043-9
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 70 (1978), 185-188
- MSC: Primary 60J99; Secondary 60K35
- DOI: https://doi.org/10.1090/S0002-9939-1978-0478385-8
- MathSciNet review: 0478385