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.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.