@article{AIHPB_1988__24_3_367_0, author = {Barnsley, M. F. and Demko, S. G. and Elton, J. H. and Geronimo, J. S.}, title = {Invariant measures for {Markov} processes arising from iterated function systems with place-dependent probabilities}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {367--394}, publisher = {Gauthier-Villars}, volume = {24}, number = {3}, year = {1988}, mrnumber = {971099}, zbl = {0653.60057}, language = {en}, url = {http://archive.numdam.org/item/AIHPB_1988__24_3_367_0/} }
TY - JOUR AU - Barnsley, M. F. AU - Demko, S. G. AU - Elton, J. H. AU - Geronimo, J. S. TI - Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities JO - Annales de l'I.H.P. Probabilités et statistiques PY - 1988 SP - 367 EP - 394 VL - 24 IS - 3 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPB_1988__24_3_367_0/ LA - en ID - AIHPB_1988__24_3_367_0 ER -
%0 Journal Article %A Barnsley, M. F. %A Demko, S. G. %A Elton, J. H. %A Geronimo, J. S. %T Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities %J Annales de l'I.H.P. Probabilités et statistiques %D 1988 %P 367-394 %V 24 %N 3 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPB_1988__24_3_367_0/ %G en %F AIHPB_1988__24_3_367_0
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, pp. 367-394. http://archive.numdam.org/item/AIHPB_1988__24_3_367_0/
[B] Invariant Set Under Iteration of Rational Functions, Arkiv für Matematik, Vol. 6, 1965, pp. 103-144. | MR | Zbl
,[BD] Iterated Functions Systems and the Global Construction of Fractals, Proc. R. Soc. London, Vol. A 399, 1985, pp. 243-275. | MR | Zbl
and ,[BGM] Function Weighted Measures and Orthogonal Polynomials on Julia Sets, Const. Approx. (to appear). | Zbl
, and ,[BE] Stationary Attractive Measures for a Class of Markov Chains Arising from Function Iteration, Adv. Appl. Prob., March 1988 (to appear).
and ,[BM] A Stochastic Model with Applications to Learning, Ann. Math. Statist., Vol. 24, 1953, pp. 449-585. | MR | Zbl
and ,[DHN] Construction of Fractal Objects with Iterated Function Systems, SIGGRAPH '85 Proceedings, 1985, pp. 271-278.
, and ,[DF] Invariant Probabilities for Certain Markov Processes, Ann. Math. Stat., Vol. 37, 1966, pp. 837-848. | MR | Zbl
and ,[DS] 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 | Zbl
and ,[DoF] Sur des chaines à liaisons complètes, Bull. Soc. Math. de France, Vol. 65, 1937, pp. 132-148. | JFM | Numdam | MR | Zbl
and ,[DuS]
and , Linear Operators, Wiley, New York, 1958.[DU] Vector Measures, American Mathematical Society, 1977. | MR | Zbl
and ,[E] An Ergodic Theorem for Iterated Maps, Ergod. Th. and Dyna Sys., Vol. 7, 1987 (to appear). | MR | Zbl
,[FLM] An Invariant Measure for Rational Maps, Bol. Soc. Bras. Mat., Vol. 14, 1983, pp. 45-62. | MR | Zbl
, and ,[G] The Theory of Matrices, Chelsea, New York, 1977.
,[H] Fractals and Self-Similarity, Indiana U. J. of Math., Vol. 30, 1981, pp. 713-747. | MR | Zbl
,[HS] Real and Abstract Analysis, Springer-Verlag, New York, 1969. | MR | Zbl
and ,[IT] On a Class of Operators Occurring in the Theory of Chains of Infinite Order, Can. J. Math., Vol. 11, 1959, pp. 112-121. | MR | Zbl
,[ITM] Sur certaines chaines à liaisons complètes, C. R. Acad. Sci. Paris, T. 227, 1948, pp. 667-669. [J] , Irreducible Markov Operators on C(S), Proc. Am. Math. Soc., Vol. 24, 1970, pp. 366-370. | MR
and ,[JS] Irreducible Almost Periodic Markov Operators, J. Math. Mech., Vol. 18, 1969, p. 1043-1057. | MR | Zbl
and ,[K] Some Random Walks Arising in Leaening Models, Pac. J. Math., Vol. 3, 1953, pp. 725-756. | MR | Zbl
,[Kr] Ergodic Theorems, de Gruyter, Berlin, 1985. | MR | Zbl
,[L] Entropy Properties of Rational Endomorphisms of the Riemann Sphere, Ergod. Th. Dynam. Sys., Vol. 3, 1983, pp. 351-385. | MR | Zbl
,[Lor] Approximation of Functions, Holt, Reinhardt, and Winston, N. Y., 1966. | MR | Zbl
,[LY] On the Existence of Invariant Measures for Piecewise Monotonic Transformations, Trans. Am. Math. Soc., Vol. 186, 1973, pp. 481-488. | MR | Zbl
and ,[NJ General Irreducible Markov Chains and Non-Negative Operators, Cambridge U. Press, Cambridge, 1985. | Zbl
,[OM] Sur les chaînes de variables statistiques, Bull. Soc. Math. de France, Vol. 59, 1935, pp. 174-192. | JFM | Zbl
and ,[R] Equicontinuous Markov Operators, Theor. Prob. and its Appl., Vol. 9, 1964, pp. 180-197 (translation of Theor. Verojatnost. i Primenen). | MR | Zbl
,[S] Convergence Theorems for Weakly Almost Periodic Markov Operators, Israel J. Math., Vol. 19, 1974, pp. 246-255. | MR | Zbl
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