Convergence of iterates of Lasota-Mackey-Tyrcha operators

Wojciech Bartoszek

Annales Polonici Mathematici (1996)

  • Volume: 63, Issue: 3, page 281-292
  • ISSN: 0066-2216

Abstract

top
We provide sufficient and necessary conditions for asymptotic periodicity of iterates of strong Feller stochastic operators.

How to cite

top

Wojciech Bartoszek. "Convergence of iterates of Lasota-Mackey-Tyrcha operators." Annales Polonici Mathematici 63.3 (1996): 281-292. <http://eudml.org/doc/262602>.

@article{WojciechBartoszek1996,
abstract = {We provide sufficient and necessary conditions for asymptotic periodicity of iterates of strong Feller stochastic operators.},
author = {Wojciech Bartoszek},
journal = {Annales Polonici Mathematici},
keywords = {stochastic (Markov) operator; strong Feller kernel; stationary density; asymptotic periodicity; iterates of strong Feller stochastic operators},
language = {eng},
number = {3},
pages = {281-292},
title = {Convergence of iterates of Lasota-Mackey-Tyrcha operators},
url = {http://eudml.org/doc/262602},
volume = {63},
year = {1996},
}

TY - JOUR
AU - Wojciech Bartoszek
TI - Convergence of iterates of Lasota-Mackey-Tyrcha operators
JO - Annales Polonici Mathematici
PY - 1996
VL - 63
IS - 3
SP - 281
EP - 292
AB - We provide sufficient and necessary conditions for asymptotic periodicity of iterates of strong Feller stochastic operators.
LA - eng
KW - stochastic (Markov) operator; strong Feller kernel; stationary density; asymptotic periodicity; iterates of strong Feller stochastic operators
UR - http://eudml.org/doc/262602
ER -

References

top
  1. [1] K. Baron and A. Lasota, Asymptotic properties of Markov operators defined by Volterra type integrals, Ann. Polon. Math. 57 (1993), 161-175. Zbl0839.47021
  2. [2] W. Bartoszek, Asymptotic stability of the iterates of contractions on Banach lattices, in: Proc. Internat. Conf. on Function Spaces, Poznań 1986, J. Musielak (ed.), Teubner, Leipzig, 1987, 153-157. 
  3. [3] W. Bartoszek, Asymptotic periodicity of the iterates of positive contractions on Banach lattices, Studia Math. 91 (1988), 179-188. Zbl0675.47025
  4. [4] W. Bartoszek, Asymptotic properties of the iterates of stochastic operators on (AL) Banach lattices, Ann. Polon. Math. 52 (1990), 165-173. Zbl0719.47022
  5. [5] A. Lasota, T. Y. Li and J. A. Yorke, Asymptotic periodicity of the iterates of Markov operators, Trans. Amer. Math. Soc. 286 (1984), 751-764. Zbl0564.47015
  6. [6] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer, New York, 1993. Zbl0784.58005
  7. [7] A. Lasota, M. C. Mackey and J. Tyrcha, The statistical dynamics of recurrent biological events, J. Math. Biology 30 (1992), 775-800. Zbl0763.92001
  8. [8] S. Łojasiewicz, An Introduction to the Theory of Real Functions, Wiley, Chichester, 1988. Zbl0653.26001
  9. [9] F. Räbiger, Attractors and asymptotic periodicity of positive operators on Banach lattices, Tübingen Ber. Funktionanal. 3 (1993/94), 184-203. 
  10. [10] D. Revuz, Markov Chains, Elsevier, Amsterdam, 1984. 
  11. [11] H. H. Schaefer, Banach Lattices and Positive Operators, Springer, New York, 1974. Zbl0296.47023

NotesEmbed ?

top

You must be logged in to post comments.