no. 3
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
corrigé par Erratum Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities 
@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},
     year = {1988},
     publisher = {Gauthier-Villars},
     volume = {24},
     number = {3},
     mrnumber = {971099},
     zbl = {0653.60057},
     language = {en},
     url = {https://www.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  - https://www.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 https://www.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. https://www.numdam.org/item/AIHPB_1988__24_3_367_0/

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

[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. | Zbl | MR

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

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

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

[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. | Zbl | MR

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

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

[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. | Zbl | MR

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

[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. | Zbl | MR

[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

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

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

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

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

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

[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. | Zbl | MR

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

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

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

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