Barnsley, M. F.; Demko, S. G.; Elton, J. H.; Geronimo, J. S.
Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities
Annales de l'I.H.P. Probabilités et statistiques, Tome 24 (1988) no. 3 , p. 367-394
Zbl 0653.60057 | MR 971099 | 1 citation dans Numdam
⇒ un erratum à cet article Erratum Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities
URL stable : http://www.numdam.org/item?id=AIHPB_1988__24_3_367_0

Bibliographie

[B] H. Brolin, Invariant Set Under Iteration of Rational Functions, Arkiv für Matematik, Vol. 6, 1965, pp. 103-144. MR 194595 | Zbl 0127.03401

[BD] M.F. Barnsley and S. Demko, Iterated Functions Systems and the Global Construction of Fractals, Proc. R. Soc. London, Vol. A 399, 1985, pp. 243-275. MR 799111 | Zbl 0588.28002

[BGM] D. Bessis, J.S. Geronimo and P. Moussa, Function Weighted Measures and Orthogonal Polynomials on Julia Sets, Const. Approx. (to appear). Zbl 0635.42021

[BE] M.F. Barnsley and J. Elton, Stationary Attractive Measures for a Class of Markov Chains Arising from Function Iteration, Adv. Appl. Prob., March 1988 (to appear).

[BM] R.R. Bush and F. Mosteller, A Stochastic Model with Applications to Learning, Ann. Math. Statist., Vol. 24, 1953, pp. 449-585. MR 58909 | Zbl 0051.35604

[DHN] S. Demko, L. Hodges and B. Naylor, Construction of Fractal Objects with Iterated Function Systems, SIGGRAPH '85 Proceedings, 1985, pp. 271-278.

[DF] L. Dubins and D. Freedman, Invariant Probabilities for Certain Markov Processes, Ann. Math. Stat., Vol. 37, 1966, pp. 837-848. MR 193668 | Zbl 0147.16404

[DS] P. Diacones and M. Shahshahani, Products of Random Matrices and Computer Image generation, in Random Matrices and Their Applications, Vol. 50, Cont. Math. A.M.S., Providence, R.I., 1986. MR 841091 | Zbl 0601.60066

[DoF] W. Doeblin and R. Fortet, Sur des chaines à liaisons complètes, Bull. Soc. Math. de France, Vol. 65, 1937, pp. 132-148. Numdam | JFM 63.1077.05 | MR 1505076 | Zbl 0018.03303

[DuS] N. Dunford and J. Schwartz, Linear Operators, Wiley, New York, 1958.

[DU] J. Diestel and J.J. Uhl, Vector Measures, American Mathematical Society, 1977. MR 453964 | Zbl 0369.46039

[E] J.H. Elton, An Ergodic Theorem for Iterated Maps, Ergod. Th. and Dyna Sys., Vol. 7, 1987 (to appear). MR 922361 | Zbl 0621.60039

[FLM] A. Freire, A. Lopes and R. Mañé, An Invariant Measure for Rational Maps, Bol. Soc. Bras. Mat., Vol. 14, 1983, pp. 45-62. MR 736568 | Zbl 0568.58027

[G] F.R. Gantmacher, The Theory of Matrices, Chelsea, New York, 1977.

[H] J. Hutchinson, Fractals and Self-Similarity, Indiana U. J. of Math., Vol. 30, 1981, pp. 713-747. MR 625600 | Zbl 0598.28011

[HS] E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer-Verlag, New York, 1969. MR 367121 | Zbl 0225.26001

[IT] C. Iionescu Tulcea, On a Class of Operators Occurring in the Theory of Chains of Infinite Order, Can. J. Math., Vol. 11, 1959, pp. 112-121. MR 101569 | Zbl 0086.12001

[ITM] C. Ionescu and G. Marinescu, Sur certaines chaines à liaisons complètes, C. R. Acad. Sci. Paris, T. 227, 1948, pp. 667-669. [J] B. Jamison, Irreducible Markov Operators on C(S), Proc. Am. Math. Soc., Vol. 24, 1970, pp. 366-370. MR 27468

[JS] B. Jamison and R. Sine, Irreducible Almost Periodic Markov Operators, J. Math. Mech., Vol. 18, 1969, p. 1043-1057. MR 242257 | Zbl 0266.60056

[K] S. Karlin, Some Random Walks Arising in Leaening Models, Pac. J. Math., Vol. 3, 1953, pp. 725-756. MR 58910 | Zbl 0051.10603

[Kr] U. Krengel, Ergodic Theorems, de Gruyter, Berlin, 1985. MR 797411 | Zbl 0575.28009

[L] M.J. Ljubich, Entropy Properties of Rational Endomorphisms of the Riemann Sphere, Ergod. Th. Dynam. Sys., Vol. 3, 1983, pp. 351-385. MR 741393 | Zbl 0537.58035

[Lor] G.G. Lorentz, Approximation of Functions, Holt, Reinhardt, and Winston, N. Y., 1966. MR 213785 | Zbl 0153.38901

[LY] A. Lasota and J.A. Yorke, On the Existence of Invariant Measures for Piecewise Monotonic Transformations, Trans. Am. Math. Soc., Vol. 186, 1973, pp. 481-488. MR 335758 | Zbl 0298.28015

[NJ E. Nummelin, General Irreducible Markov Chains and Non-Negative Operators, Cambridge U. Press, Cambridge, 1985. Zbl 0551.60066

[OM] O. Onicescu and G. Mihoc, Sur les chaînes de variables statistiques, Bull. Soc. Math. de France, Vol. 59, 1935, pp. 174-192. JFM 61.0563.02 | Zbl 0012.02804

[R] M. Rosenblatt, Equicontinuous Markov Operators, Theor. Prob. and its Appl., Vol. 9, 1964, pp. 180-197 (translation of Theor. Verojatnost. i Primenen). MR 171318 | Zbl 0133.40101

[S] R. Sine, Convergence Theorems for Weakly Almost Periodic Markov Operators, Israel J. Math., Vol. 19, 1974, pp. 246-255. MR 372159 | Zbl 0309.60048