Markov operators arising from graph directed constructions of iterated function systems are considered. Exponential convergence to an invariant measure is proved.
@article{bwmeta1.element.doi-10_1515_amsil-2015-0011,
author = {Maciej \'Sl\k eczka},
title = {Exponential Convergence For Markov Systems},
journal = {Annales Mathematicae Silesianae},
volume = {29},
year = {2015},
pages = {139-149},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0011}
}
Maciej Ślęczka. Exponential Convergence For Markov Systems. Annales Mathematicae Silesianae, Tome 29 (2015) pp. 139-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0011/
[1] 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, Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), 367–394. | Zbl 0653.60057
[2] Hairer M., Exponential mixing properties of stochastic PDEs through asymptotic coupling, Probab. Theory Related Fields 124 (2002), 345–380. | Zbl 1032.60056
[3] Hairer M., Mattingly J., Scheutzow M., Asymptotic coupling and a general form of Harris’ theorem with applications to stochastic delay equations, Probab. Theory Related Fields 149 (2011), no. 1, 223–259. | Zbl 1238.60082
[4] Horbacz K., Szarek T., Irreducible Markov systems on Polish spaces, Studia Math. 177 (2006), no. 3, 285–295. | Zbl 1108.60066
[5] Horbacz K.,Ślęczka M., Law of large numbers for random dynamical systems, Preprint 2013, arXiv:1304.6863. | Zbl 1335.60036
[6] Kapica R.,Ślęczka M., Random iteration with place dependent probabilities, Preprint 2012, arXiv:1107.0707v2.
[7] Mauldin R.D., Williams S.C., Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc. 309 (1988), 811–829. | Zbl 0706.28007
[8] Mauldin R.D., Urbański M., Graph directed Markov systems: geometry and dynamics of limit sets, Cambridge University Press, Cambridge, 2003. | Zbl 1033.37025
[9] Rachev S.T., Probability metrics and the stability of stochastic models, John Wiley, New York, 1991. | Zbl 0744.60004
[10]Ślęczka M., The rate of convergence for iterated function systems, Studia Math. 205 (2011), no. 3, 201–214. | Zbl 1244.60068
[11] Werner I., Ergodic theorem for contractive Markov systems, Nonlinearity 17 (2004), 2303–2313. | Zbl 1100.60039
[12] Werner I., Contractive Markov systems, J. London Math. Soc. (2) 71 (2005), 236–258. | Zbl 1071.60064
[13] Wojewódka H. Exponential rate of convergence for some Markov operators, Statist. Probab. Lett. 83 (2013), 2337–2347.[WoS] | Zbl 1291.60156