Exponential Convergence For Markov Systems

• Autorzy: Maciej Ślęczka
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Markov operator; invariant measure

Kategorie tematyczne

• 37A25: Ergodicity, mixing, rates of mixing
• 60J05: Discrete-time Markov processes on general state spaces

• Wydawca: De Gruyter Open
• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2015
• Tom: 29
• Numer: 1
• Strony: 139-149

Daty

wydano

2015-09-01

otrzymano

2015-05-28

poprawiono

2015-06-15

online

2015-09-30

Twórcy

autor

Maciej Ślęczka

• Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [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.
• [2] Hairer M., Exponential mixing properties of stochastic PDEs through asymptotic coupling, Probab. Theory Related Fields 124 (2002), 345–380.
• [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.
• [4] Horbacz K., Szarek T., Irreducible Markov systems on Polish spaces, Studia Math. 177 (2006), no. 3, 285–295.
• [5] Horbacz K.,Ślęczka M., Law of large numbers for random dynamical systems, Preprint 2013, arXiv:1304.6863.
• [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.
• [8] Mauldin R.D., Urbański M., Graph directed Markov systems: geometry and dynamics of limit sets, Cambridge University Press, Cambridge, 2003.
• [9] Rachev S.T., Probability metrics and the stability of stochastic models, John Wiley, New York, 1991.
• [10]Ślęczka M., The rate of convergence for iterated function systems, Studia Math. 205 (2011), no. 3, 201–214.
• [11] Werner I., Ergodic theorem for contractive Markov systems, Nonlinearity 17 (2004), 2303–2313.
• [12] Werner I., Contractive Markov systems, J. London Math. Soc. (2) 71 (2005), 236–258.
• [13] Wojewódka H. Exponential rate of convergence for some Markov operators, Statist. Probab. Lett. 83 (2013), 2337–2347.[WoS]

Identyfikatory

DOI

10.1515/amsil-2015-0011