Exponential Convergence For Markov Systems

Maciej Ślęczka

Annales Mathematicae Silesianae (2015)

  • Volume: 29, Issue: 1, page 139-149
  • ISSN: 0860-2107

Abstract

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Markov operators arising from graph directed constructions of iterated function systems are considered. Exponential convergence to an invariant measure is proved.

How to cite

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Maciej Ślęczka. "Exponential Convergence For Markov Systems." Annales Mathematicae Silesianae 29.1 (2015): 139-149. <http://eudml.org/doc/276841>.

@article{MaciejŚlęczka2015,
abstract = {Markov operators arising from graph directed constructions of iterated function systems are considered. Exponential convergence to an invariant measure is proved.},
author = {Maciej Ślęczka},
journal = {Annales Mathematicae Silesianae},
keywords = {Markov operator; invariant measure},
language = {eng},
number = {1},
pages = {139-149},
title = {Exponential Convergence For Markov Systems},
url = {http://eudml.org/doc/276841},
volume = {29},
year = {2015},
}

TY - JOUR
AU - Maciej Ślęczka
TI - Exponential Convergence For Markov Systems
JO - Annales Mathematicae Silesianae
PY - 2015
VL - 29
IS - 1
SP - 139
EP - 149
AB - Markov operators arising from graph directed constructions of iterated function systems are considered. Exponential convergence to an invariant measure is proved.
LA - eng
KW - Markov operator; invariant measure
UR - http://eudml.org/doc/276841
ER -

References

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  1. [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. Zbl0653.60057
  2. [2] Hairer M., Exponential mixing properties of stochastic PDEs through asymptotic coupling, Probab. Theory Related Fields 124 (2002), 345–380. Zbl1032.60056
  3. [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. Zbl1238.60082
  4. [4] Horbacz K., Szarek T., Irreducible Markov systems on Polish spaces, Studia Math. 177 (2006), no. 3, 285–295. Zbl1108.60066
  5. [5] Horbacz K.,Ślęczka M., Law of large numbers for random dynamical systems, Preprint 2013, arXiv:1304.6863. Zbl1335.60036
  6. [6] Kapica R.,Ślęczka M., Random iteration with place dependent probabilities, Preprint 2012, arXiv:1107.0707v2. 
  7. [7] Mauldin R.D., Williams S.C., Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc. 309 (1988), 811–829. Zbl0706.28007
  8. [8] Mauldin R.D., Urbański M., Graph directed Markov systems: geometry and dynamics of limit sets, Cambridge University Press, Cambridge, 2003. Zbl1033.37025
  9. [9] Rachev S.T., Probability metrics and the stability of stochastic models, John Wiley, New York, 1991. Zbl0744.60004
  10. [10]Ślęczka M., The rate of convergence for iterated function systems, Studia Math. 205 (2011), no. 3, 201–214. Zbl1244.60068
  11. [11] Werner I., Ergodic theorem for contractive Markov systems, Nonlinearity 17 (2004), 2303–2313. Zbl1100.60039
  12. [12] Werner I., Contractive Markov systems, J. London Math. Soc. (2) 71 (2005), 236–258. Zbl1071.60064
  13. [13] Wojewódka H. Exponential rate of convergence for some Markov operators, Statist. Probab. Lett. 83 (2013), 2337–2347.[WoS] Zbl1291.60156

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