Asymptotic periodicity of some stochastically perturbed dynamical systems
Annales de l'I.H.P. Probabilités et statistiques, Volume 28 (1992) no. 2, p. 165-178
@article{AIHPB_1992__28_2_165_0,
     author = {Komorowski, Tomasz},
     title = {Asymptotic periodicity of some stochastically perturbed dynamical systems},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {28},
     number = {2},
     year = {1992},
     pages = {165-178},
     zbl = {0747.60063},
     mrnumber = {1162571},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1992__28_2_165_0}
}
Komorowski, T. Asymptotic periodicity of some stochastically perturbed dynamical systems. Annales de l'I.H.P. Probabilités et statistiques, Volume 28 (1992) no. 2, pp. 165-178. http://www.numdam.org/item/AIHPB_1992__28_2_165_0/

[1] S. Foguel, The Ergodic Theory of Markov Processes, van Nostrand, 1969. | MR 261686 | Zbl 0282.60037

[2] M.J. Kushner, Stochastic Stability and Control, Academic Press, New York, 1967. | MR 216894 | Zbl 0244.93065

[3] M.J. Kushner, Introduction to Stochastic Control Theory, Holt, Reinhart and Winston, New York, 1971. | MR 280248 | Zbl 0293.93018

[4] A. Lasota and J. Tyrcha, On the Strong Convergence to Equilibrium for Randomly Perturbed Dynamical Systems, An. Polon. Math. (to appear). | MR 1110663 | Zbl 0722.60068

[5] S. Meyn, Ergodic Theorems for Discrete Time Stochastic Systems Using a Stochastic Lyapunov Function, S.I.A.M. J. Control Optimization, Vol. 27, 1989, pp. 1409-1439. | MR 1022436 | Zbl 0681.60067

[6] A. Mokkadem, Propriétés de mélange des processus autorégressifs polynomiaux, Ann. Inst. Henri Poincaré, Vol. 26, 1990, pp. 219-260. | Numdam | MR 1063750 | Zbl 0706.60040

[7] E. Nummelin, General Irreducible Markov Chains and Nonnegative Operators, Cambridge Univ. Press, 1984. | MR 776608 | Zbl 0551.60066

[8] A.G. Pakes, Some Conditions for Ergodicity and Recurrence of Markov chains, Operational Research, Vol. 17, 1969, pp. 1058-1061. | MR 260035 | Zbl 0183.46902

[9] M. Rosenblatt, Markov Processes: Structure and Asymptotic Behavior, Springer-Verlag, Berlin, Heidelberg, New York 1971. | MR 329037 | Zbl 0236.60002

[10] J. Socala, On the Existence of Invariant Density for Markov Operators, Ann. Polon. Math., Vol. 48, 1988, pp. 51-56. | MR 931389 | Zbl 0657.60089

[11] J. Tyrcha, Asymptotic Stability in a Generalized Probabilistic/Deterministic Model of the Cell Cycle, J. Math. Biology, Vol. 26, 1988, pp. 465-475. | MR 966316 | Zbl 0716.92017

[12] U. Krengel, Ergodic Theorems, Walter de Gruyler, Berlin-New York, 1985. | MR 797411 | Zbl 0575.28009

[13] A. Lasota and M.C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, 1985. | MR 832868 | Zbl 0606.58002