@article{PSMIR_1993___2_A9_0,
author = {Peign\'e, Marc},
title = {Iterated {Function} {Systems} and {Spectral} {Decomposition} of the {Associated} {Markov} {Operator}},
journal = {Publications de l'Institut de recherche math\'ematiques de Rennes},
eid = {9},
pages = {1--28},
year = {1993},
publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
number = {2},
mrnumber = {1347702},
language = {en},
url = {https://www.numdam.org/item/PSMIR_1993___2_A9_0/}
}
TY - JOUR AU - Peigné, Marc TI - Iterated Function Systems and Spectral Decomposition of the Associated Markov Operator JO - Publications de l'Institut de recherche mathématiques de Rennes PY - 1993 SP - 1 EP - 28 IS - 2 PB - Département de Mathématiques et Informatique, Université de Rennes UR - https://www.numdam.org/item/PSMIR_1993___2_A9_0/ LA - en ID - PSMIR_1993___2_A9_0 ER -
%0 Journal Article %A Peigné, Marc %T Iterated Function Systems and Spectral Decomposition of the Associated Markov Operator %J Publications de l'Institut de recherche mathématiques de Rennes %D 1993 %P 1-28 %N 2 %I Département de Mathématiques et Informatique, Université de Rennes %U https://www.numdam.org/item/PSMIR_1993___2_A9_0/ %G en %F PSMIR_1993___2_A9_0
Peigné, Marc. Iterated Function Systems and Spectral Decomposition of the Associated Markov Operator. Publications de l'Institut de recherche mathématiques de Rennes, Fascicule de probabilités, no. 2 (1993), article no. 9, 28 p.. https://www.numdam.org/item/PSMIR_1993___2_A9_0/
[1] , Iterated function systems and multiplicative ergodic theory. preprint. | Zbl
[2] , , , Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities. Ann. de l'Institut Henri Poincaré, vol. 24, n°3, (1988), p. 367-394. | Zbl | MR | Numdam
[3] , A new class of Markov processes for image encoding. Adv. Appl. Prob. 20, (1988), p. 14-32. | Zbl | MR
[4] , Random walks generated by affine Mappings. Journal of theorical probability, vol. 1, n°3, (1988). | Zbl | MR
[5] , Fonctions harmoniques pour un opérateur de transition et applications. Bulletin soc. Math. France , 118, (1990), p. 273-310. | Zbl | MR | Numdam
[6] , Sur des chaînes a liasons complètes, Bull. Soc. Math. de France , Vol 65, (1937), p. 132-148. | MR | JFM | Numdam
[7] , Invariant probabilities for certains Markov processes. Ann. Math. Stat. 37, (196), p. 837-848 | Zbl | MR
[8] , Product of random matrices and computer image generation. Random Matrices and their applications. 50, Cont. Math A.M.S., Providence, R.I (1986) | Zbl | MR
[9] An ergodic theorem for iterated maps. Ergod. Th. and Dynam Syst., n°7, (1987), p. 481-488. | Zbl | MR
[10] , , Random walks in a quater plane with zero drifts. I Ergodicity and null recurrence. Ann. Inst. Henri Poincaré, Vol. 28, n°2, (1992), p. 179-194. | Zbl | MR | Numdam
[11] , Products of random matrices. Ann. Math. Statis., n°31, (1960), p. 457-469. | Zbl | MR
[12] Implicit renewal theory and tails of solutions of random equations. The Annals of Applied Probability, Vol 1, n°1, (1991), p. 126-166. | Zbl | MR
[13] A central limit theorem for the group of linear transformation of the real axis Soviet Math. Doklady, Vol 15, n°6, (1974), p. 1512-1515. | Zbl
[14] , Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov. Ann. Inst. Henri Poincaré, Vol. 24, n°1, (1988), p. 73-98. | Zbl | MR | Numdam
[15] , Asymptotic winding of the geodesic flow on modular surfaces and continuous fractions. Ann. scient. Ec. Norm. Sup., 4ème série, t. 26, 1993, p. 23-50. | Zbl | MR | Numdam
[16] , Frontières de Furstenberg, propriétés de contraction et théorèmes de convergence. Zeït für Wahr., n°69, (1985), p. 187-242. | Zbl
[17] Etude d'opérateurs quasi-compacts positifs. Applications aux opérareurs de transfert. To appear in Ann. Inst. Henri Poincaré, | Zbl | Numdam
[18] , Martingale limit theory and its applications. New York Academic Press(1980) | Zbl | MR
[19] Décomposition spectrale des opérateurs de Doeblin-Fortet. Proceeding of the A.M.S, n°69, (1993), p. 627-634
[20] . Fractals and self-similarity. Indiana U. J. of Math., 30, (1981), p. 713-747. | Zbl | MR
[21] On a class of operators occuring in the theory of chains of infinite order. Can. J. Math, Vol 11, 1959, p.112-121 | Zbl | MR
[22] , . Sur certaines chaînes à liaisons complètes. C.R.A.S., 227, (1948), p. 667-669 | Zbl | MR
[23] Asymptotic behaviour of successive iterates of continuous functions under a Markov operator. J. of Math. Analysis and Applications, t. 9, (1964), p. 203-214. | Zbl | MR
[24] Some random walks Arising in Learning models. Pac. J. of Math., 3, (1953, p. 725-756. | Zbl | MR
[25] Théorèmes de renouvellement pour les produits de matrices aléatoires. Equations aux différences aléatoires. Séminaires de Rennes
[26] Marche aléatoire sur le semi-groupe des contractions de . Cas de la marche aléatoire sur avec chocs élastiques en zéro. Ann. Inst. Henri Poincaré, Vol. 25, n°4, (1989), p. 483-502. | Zbl | MR | Numdam
[27] Bases mathématiques du calcul des probabilités. Masson et Cie, 1964. | Zbl | MR
[28] Markov processes and learning models. Academic Press, 1972. | Zbl | MR
[29] General irreductible Markov chains and non-negative operators. Cambridge U. Press, Cambridge (1985). | Zbl
[30] Marches de Markov sur le semi-groupe des contractions de . Ann. Inst. Henri Poincaré, Vol 28, n°1, (1992), p. 63-94. | Zbl | MR | Numdam
[31] Théorie spectrale d'un opérateur de transition sur un espace compact. Ann. Inst. Henri Poincaré, Vol. 28, n°2, (1992), p. 281-309. | Zbl | MR | Numdam
[32] Fonctions harmoniques et théorèmes limites pour les marches aléatoires sur les groupes. Bull. Soc. Math. de France, Vol 54, (1977)
[33] Equicontinuous Markov operators. Theor. Prob. and its Appl., vol. 9, (1969), p. 180-197. | Zbl | MR
[34] Markov chains. North Holland Pub. Comp., 1975 | Zbl | MR






