Dynamical systems with multiplicative perturbations: the strong convergence of measures

Katarzyna Horbacz

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 1, page 85-93
  • ISSN: 0066-2216

Abstract

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We give sufficient conditions for the strong asymptotic stability of the distributions of dynamical systems with multiplicative perturbations. We apply our results to iterated function systems.

How to cite

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Katarzyna Horbacz. "Dynamical systems with multiplicative perturbations: the strong convergence of measures." Annales Polonici Mathematici 58.1 (1993): 85-93. <http://eudml.org/doc/262256>.

@article{KatarzynaHorbacz1993,
abstract = {We give sufficient conditions for the strong asymptotic stability of the distributions of dynamical systems with multiplicative perturbations. We apply our results to iterated function systems.},
author = {Katarzyna Horbacz},
journal = {Annales Polonici Mathematici},
keywords = {dynamical system; Markov operator; strong asymptotic stability; iterated function system; multiplicative stochastic perturbations; strong asymptotical stability; iterated function systems},
language = {eng},
number = {1},
pages = {85-93},
title = {Dynamical systems with multiplicative perturbations: the strong convergence of measures},
url = {http://eudml.org/doc/262256},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Katarzyna Horbacz
TI - Dynamical systems with multiplicative perturbations: the strong convergence of measures
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 1
SP - 85
EP - 93
AB - We give sufficient conditions for the strong asymptotic stability of the distributions of dynamical systems with multiplicative perturbations. We apply our results to iterated function systems.
LA - eng
KW - dynamical system; Markov operator; strong asymptotic stability; iterated function system; multiplicative stochastic perturbations; strong asymptotical stability; iterated function systems
UR - http://eudml.org/doc/262256
ER -

References

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  1. [1] M. F. Barnsley and S. Demko, Iterated function systems and the global construction of fractals, Proc. Roy. Soc. London Ser. A 399 (1985), 243-275. Zbl0588.28002
  2. [2] M. F. Barnsley, V. Ervin, D. Hardin and J. Lancaster, Solution of an inverse problem for fractals and other sets, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), 1975-1977. Zbl0613.28008
  3. [3] K. Horbacz, Dynamical systems with multiplicative perturbations, Ann. Polon. Math. 50 (1989), 93-102. Zbl0687.60064
  4. [4] K. Horbacz, Asymptotic stability of dynamical systems with multiplicative perturbations, ibid. 50 (1989), 209-218. Zbl0703.47033
  5. [5] A. Lasota and J. Tyrcha, On the strong convergence to equilibrium for randomly perturbed dynamical systems, ibid. 53 (1991), 79-89. Zbl0722.60068
  6. [6] A. Lasota and M. C. Mackey, Stochastic perturbation of dynamical systems: The weak convergence of measures, J. Math. Anal. Appl. 138 (1989), 232-248. Zbl0668.93081
  7. [7] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge Univ. Press, Cambridge 1985. Zbl0606.58002
  8. [8] M. Podhorodyński, Stability of Markov processes, Univ. Iagell. Acta Math. 27 (1988), 285-296. 

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