Randomly connected dynamical systems - asymptotic stability

Katarzyna Horbacz

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 1, page 31-50
  • ISSN: 0066-2216

Abstract

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We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.

How to cite

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Katarzyna Horbacz. "Randomly connected dynamical systems - asymptotic stability." Annales Polonici Mathematici 68.1 (1998): 31-50. <http://eudml.org/doc/270275>.

@article{KatarzynaHorbacz1998,
abstract = {We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.},
author = {Katarzyna Horbacz},
journal = {Annales Polonici Mathematici},
keywords = {dynamical systems; Markov operator; asymptotic stability; evolution of measures; randomly chosen dynamical systems; invariant measure; transition operator},
language = {eng},
number = {1},
pages = {31-50},
title = {Randomly connected dynamical systems - asymptotic stability},
url = {http://eudml.org/doc/270275},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Katarzyna Horbacz
TI - Randomly connected dynamical systems - asymptotic stability
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 1
SP - 31
EP - 50
AB - We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.
LA - eng
KW - dynamical systems; Markov operator; asymptotic stability; evolution of measures; randomly chosen dynamical systems; invariant measure; transition operator
UR - http://eudml.org/doc/270275
ER -

References

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  1. [1] R. Fortet et B. Mourier, Convergence de la répartition empirique vers la répartition théorétique, Ann. Sci. École Norm. Sup. 70 (1953), 267-285. Zbl0053.09601
  2. [2] K. Horbacz, Dynamical systems with multiplicative perturbations: The strong convergence of measures, Ann. Polon. Math. 58 (1993), 85-93. Zbl0782.47007
  3. [3] W. Jarczyk and A. Lasota, Invariant measures for fractals and dynamical systems, to appear. 
  4. [4] A. Lasota, From fractals to stochastic differential equations, to appear. 
  5. [5] A. Lasota and M. C. Mackey, Noise and statistical periodicity, Physica D 28 (1987), 143-154. Zbl0645.60068
  6. [6] A. Lasota and M. C. Mackey, Why do cells divide?, to appear. 
  7. [7] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise - Stochastic Aspect of Dynamics, Springer, New York, 1994. Zbl0784.58005
  8. [8] A. Lasota and J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynamics 2 (1994), 41-77. Zbl0804.47033
  9. [9] T. Szarek, Iterated function systems depending on previous transformation, Univ. Iagell. Acta Math., to appear. Zbl0888.47016

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