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Asymptotic periodicity of some stochastically perturbed dynamical systems

T. Komorowski

Annales de l'I.H.P. Probabilités et statistiques (1992)

  • Volume: 28, Issue: 2, page 165-178
  • ISSN: 0246-0203

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Komorowski, T.. "Asymptotic periodicity of some stochastically perturbed dynamical systems." Annales de l'I.H.P. Probabilités et statistiques 28.2 (1992): 165-178. <http://eudml.org/doc/77428>.

@article{Komorowski1992,
author = {Komorowski, T.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {difference stochastic equation; asymptotic periodicity; asymptotic stability; model of cell cycle},
language = {eng},
number = {2},
pages = {165-178},
publisher = {Gauthier-Villars},
title = {Asymptotic periodicity of some stochastically perturbed dynamical systems},
url = {http://eudml.org/doc/77428},
volume = {28},
year = {1992},
}

TY - JOUR
AU - Komorowski, T.
TI - Asymptotic periodicity of some stochastically perturbed dynamical systems
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1992
PB - Gauthier-Villars
VL - 28
IS - 2
SP - 165
EP - 178
LA - eng
KW - difference stochastic equation; asymptotic periodicity; asymptotic stability; model of cell cycle
UR - http://eudml.org/doc/77428
ER -

References

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  1. [1] S. Foguel, The Ergodic Theory of Markov Processes, van Nostrand, 1969. Zbl0282.60037MR261686
  2. [2] M.J. Kushner, Stochastic Stability and Control, Academic Press, New York, 1967. Zbl0244.93065MR216894
  3. [3] M.J. Kushner, Introduction to Stochastic Control Theory, Holt, Reinhart and Winston, New York, 1971. Zbl0293.93018MR280248
  4. [4] A. Lasota and J. Tyrcha, On the Strong Convergence to Equilibrium for Randomly Perturbed Dynamical Systems, An. Polon. Math. (to appear). Zbl0722.60068MR1110663
  5. [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. Zbl0681.60067MR1022436
  6. [6] A. Mokkadem, Propriétés de mélange des processus autorégressifs polynomiaux, Ann. Inst. Henri Poincaré, Vol. 26, 1990, pp. 219-260. Zbl0706.60040MR1063750
  7. [7] E. Nummelin, General Irreducible Markov Chains and Nonnegative Operators, Cambridge Univ. Press, 1984. Zbl0551.60066MR776608
  8. [8] A.G. Pakes, Some Conditions for Ergodicity and Recurrence of Markov chains, Operational Research, Vol. 17, 1969, pp. 1058-1061. Zbl0183.46902MR260035
  9. [9] M. Rosenblatt, Markov Processes: Structure and Asymptotic Behavior, Springer-Verlag, Berlin, Heidelberg, New York1971. Zbl0236.60002MR329037
  10. [10] J. Socala, On the Existence of Invariant Density for Markov Operators, Ann. Polon. Math., Vol. 48, 1988, pp. 51-56. Zbl0657.60089MR931389
  11. [11] J. Tyrcha, Asymptotic Stability in a Generalized Probabilistic/Deterministic Model of the Cell Cycle, J. Math. Biology, Vol. 26, 1988, pp. 465-475. Zbl0716.92017MR966316
  12. [12] U. Krengel, Ergodic Theorems, Walter de Gruyler, Berlin-New York, 1985. Zbl0575.28009MR797411
  13. [13] A. Lasota and M.C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, 1985. Zbl0606.58002MR832868

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