Exponential Convergence For Markov Systems

[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.Search in Google Scholar

[2] Hairer M., Exponential mixing properties of stochastic PDEs through asymptotic coupling, Probab. Theory Related Fields 124 (2002), 345–380.10.1007/s004400200216Search in Google Scholar

[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.Search in Google Scholar

[4] Horbacz K., Szarek T., Irreducible Markov systems on Polish spaces, Studia Math. 177 (2006), no. 3, 285–295.Search in Google Scholar

[5] Horbacz K.,Ślęczka M., Law of large numbers for random dynamical systems, Preprint 2013, arXiv:1304.6863.Search in Google Scholar

[6] Kapica R.,Ślęczka M., Random iteration with place dependent probabilities, Preprint 2012, arXiv:1107.0707v2.Search in Google Scholar

[7] Mauldin R.D., Williams S.C., Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc. 309 (1988), 811–829.10.1090/S0002-9947-1988-0961615-4Search in Google Scholar

[8] Mauldin R.D., Urbański M., Graph directed Markov systems: geometry and dynamics of limit sets, Cambridge University Press, Cambridge, 2003.10.1017/CBO9780511543050Search in Google Scholar

[9] Rachev S.T., Probability metrics and the stability of stochastic models, John Wiley, New York, 1991.Search in Google Scholar

[10]Ślęczka M., The rate of convergence for iterated function systems, Studia Math. 205 (2011), no. 3, 201–214.Search in Google Scholar

[11] Werner I., Ergodic theorem for contractive Markov systems, Nonlinearity 17 (2004), 2303–2313.10.1088/0951-7715/17/6/016Search in Google Scholar

[12] Werner I., Contractive Markov systems, J. London Math. Soc. (2) 71 (2005), 236–258.10.1112/S0024610704006088Search in Google Scholar

[13] Wojewódka H. Exponential rate of convergence for some Markov operators, Statist. Probab. Lett. 83 (2013), 2337–2347.10.1016/j.spl.2013.05.035Search in Google Scholar