A different construction of gaussian fields from Markov chains : Dirichlet covariances
Diaconis, Persi ; Evans, Steven N.
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002), p. 863-878 / Harvested from Numdam
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@article{AIHPB_2002__38_6_863_0,
     author = {Diaconis, Persi and Evans, Steven N.},
     title = {A different construction of gaussian fields from Markov chains : Dirichlet covariances},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {38},
     year = {2002},
     pages = {863-878},
     mrnumber = {1955341},
     zbl = {1033.60049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2002__38_6_863_0}
}

Diaconis, Persi; Evans, Steven N. A different construction of gaussian fields from Markov chains : Dirichlet covariances. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) pp. 863-878. http://gdmltest.u-ga.fr/item/AIHPB_2002__38_6_863_0/

[1] J. Besag, Spatial interaction and the statistical analysis of lattice systems, J. Roy. Statist. Soc. Ser. B 36 (1974) 192-236, With discussion by D.R. Cox, A.G. Hawkes, P. Clifford, P. Whittle, K. Ord, R. Mead, J.M. Hammersley, and M.S. Bartlett and with a reply by the author. | MR 373208 | Zbl 0327.60067

[2] J. Besag, P. Green, D. Higdon, K. Mengersen, Bayesian computation and stochastic systems, Statist. Sci. 10 (1) (1995) 3-66, With comments and a reply by the authors. | MR 1349818 | Zbl 0955.62552

[3] J. Besag, P.J. Green, Spatial statistics and Bayesian computation, J. Roy. Statist. Soc. Ser. B 55 (1) (1993) 25-37. | MR 1210422 | Zbl 0800.62572

[4] J. Besag, D. Higdon, Bayesian analysis of agricultural field experiments, J. Roy. Statist. Soc. Ser. B Stat. Methodol. 61 (4) (1999) 691-746, With discussion and a reply by the authors. | MR 1722238 | Zbl 0951.62091

[5] J. Besag, C. Kooperberg, On conditional and intrinsic autoregressions, Biometrika 82 (4) (1995) 733-746. | MR 1380811 | Zbl 0899.62123

[6] A. Beurling, J. Deny, Espaces de Dirichlet. I. Le cas élémentaire, Acta Math. 99 (1958) 203-224. | MR 98924 | Zbl 0089.08106

[7] R.N. Bhattacharya, On the functional central limit theorem and the law of the iterated logarithm for Markov processes, Z. Wahrsch. Verw. Gebiete 60 (2) (1982) 185-201. | MR 663900 | Zbl 0468.60034

[8] E. Bolthausen, Random walk representations and entropic repulsion for gradient models. Preprint, 2001. | MR 1831411

[9] K. Borre, Error propagation in absolute geodetic networks - a continuous approach, in: Optimization of Design and Computation of Control Networks (Proc. Internat. Sympos., Sopron, 1977), Akad. Kiadó, Budapest, 1979, pp. 459-472.

[10] K. Borre, Plane Networks and Their Applications, Birkhäuser Boston, Boston, MA, 2001. | MR 1802805 | Zbl 0966.65123

[11] K. Borre, P. Meissl, Strength analysis of leveling-type networks. An application of random walk theory, Geodaet. Inst. Medd. 50 (1974) 80. | MR 475698

[12] D. Brydges, J. Fröhlich, T. Spencer, The random walk representation of classical spin systems and correlation inequalities, Comm. Math. Phys. 83 (1) (1982) 123-150. | MR 648362

[13] P. Diaconis, S.N. Evans, Linear functionals of eigenvalues of random matrices, Trans. Amer. Math. Soc. 353 (2001) 2615-2633. | MR 1828463 | Zbl 1008.15013

[14] P. Diaconis, D. Freedman, On the statistics of vision: the Julesz conjecture, J. Math. Psych. 24 (2) (1981) 112-138. | MR 640207 | Zbl 0494.92025

[15] P. Diaconis, M. Shahshahani, On the eigenvalues of random matrices, J. Appl. Probab. 31A (1994) 49-62. | MR 1274717 | Zbl 0807.15015

[16] M. Dozzi, Two-parameter harnesses and the Wiener process, Z. Wahrsch. Verw. Gebiete 56 (4) (1981) 507-514. | MR 621661 | Zbl 0456.60047

[17] M. Dozzi, Stochastic Processes with a Multidimensional Parameter, Longman Scientific & Technical, Harlow, 1989. | MR 991563 | Zbl 0663.60039

[18] E.B. Dynkin, Markov processes and random fields, Bull. Amer. Math. Soc. (N.S.) 3 (3) (1980) 975-999. | MR 585179 | Zbl 0519.60046

[19] E.B. Dynkin, Markov processes as a tool in field theory, J. Funct. Anal. 50 (2) (1983) 167-187. | MR 693227 | Zbl 0522.60078

[20] E.B. Dynkin, Gaussian and non-Gaussian random fields associated with Markov processes, J. Funct. Anal. 55 (3) (1984) 344-376. | MR 734803 | Zbl 0533.60061

[21] E.B. Dynkin, Polynomials of the occupation field and related random fields, J. Funct. Anal. 58 (1) (1984) 20-52. | MR 756768 | Zbl 0552.60075

[22] N. Eisenbaum, Une version sans conditionnement du théorème d'isomorphisms de Dynkin, in: Séminaire de Probabilités, XXIX, Lecture Notes in Math., 1613, Springer, Berlin, 1995, pp. 266-289. | Numdam | MR 1459468 | Zbl 0849.60075

[23] M. Fukushima, Y. Oshima, M. Takeda, Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin, 1994. | MR 1303354 | Zbl 0838.31001

[24] J. Goodman, A. Sokal, Multigrid Monte-Carlo method: conceptual foundations, Phys. Rev. D 40 (1989) 2035-2071.

[25] L. Gross, Hypercontractivity over complex manifolds, Acta Math. 182 (2) (1999) 159-206. | MR 1710181 | Zbl 0983.47026

[26] J.M. Hammersley, Harnesses, in: Proc. Fifth Berkeley Sympos. Mathematical Statistics and Probability (Berkeley, Calif., 1965/66), Vol. III: Physical Sciences, Univ. California Press, Berkeley, CA, 1967, pp. 89-117. | MR 224144

[27] K. Johansson, On random matrices from the compact classical groups, Ann. of Math. (2) 145 (1997) 519-545. | MR 1454702 | Zbl 0883.60010

[28] J.F.C. Kingman, Random variables with unsymmetrical linear regressions, Math. Proc. Cambridge Philos. Soc. 98 (2) (1985) 355-365. | MR 795900 | Zbl 0574.60014

[29] J.F.C. Kingman, The construction of infinite collections of random variables with linear regressions, Adv. Appl. Probab. (suppl.) (1986) 73-85. | MR 868509 | Zbl 0616.60005

[30] M.B. Marcus, J. Rosen, Moduli of continuity of local times of strongly symmetric Markov processes via Gaussian processes, J. Theoret. Probab. 5 (4) (1992) 791-825. | MR 1182681 | Zbl 0761.60035

[31] M.B. Marcus, J. Rosen, Moment generating functions for local times of symmetric Markov processes and random walks, in: Probability in Banach Spaces, 8 (Brunswick, ME, 1991), Birkhäuser Boston, Boston, MA, 1992, pp. 364-376. | MR 1227631 | Zbl 0788.60092

[32] M.B. Marcus, J. Rosen, p-variation of the local times of symmetric stable processes and of Gaussian processes with stationary increments, Ann. Probab. 20 (4) (1992) 1685-1713. | MR 1188038 | Zbl 0762.60069

[33] M.B. Marcus, J. Rosen, Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes, Ann. Probab. 20 (4) (1992) 1603-1684. | MR 1188037 | Zbl 0762.60068

[34] M.B. Marcus, J. Rosen, φ-variation of the local times of symmetric Lévy processes and stationary Gaussian processes, in: Seminar on Stochastic Processes, 1992 (Seattle, WA, 1992), Birkhäuser Boston, Boston, MA, 1993, pp. 209-220. | Zbl 0793.60043

[35] M.L. Mehta, Random Matrices, Academic Press, Boston, MA, 1991. | MR 1083764 | Zbl 0780.60014

[36] H.-J. Schmeisser, H. Triebel, Topics in Fourier Analysis and Function Spaces, Wiley, Chichester, 1987. | MR 891189 | Zbl 0661.46025

[37] P. Sheppard, On the Ray-Knight Markov property of local times, J. London Math. Soc. (2) 31 (2) (1985) 377-384. | MR 809960 | Zbl 0535.60070

[38] K. Symanzik, Euclidean quantum field theory, in: Jost R. (Ed.), Local Quantum Theory, Academic, New York, 1969.

[39] D. Williams, Some basic theorems on harnesses, in: Stochastic Analysis (a tribute to the memory of Rollo Davidson), Wiley, London, 1973, pp. 349-363. | MR 362565

[40] D. Ylvisaker, Prediction and design, Ann. Statist. 15 (1) (1987) 1-19. | MR 885721 | Zbl 0646.62080