On asymptotic cyclicity of doubly stochastic operators

Wojciech Bartoszek

Annales Polonici Mathematici (1999)

  • Volume: 72, Issue: 2, page 145-152
  • ISSN: 0066-2216

Abstract

top
It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports. If moreover P is Frobenius-Perron or Harris then it is strongly asymptotically cyclic.

How to cite

top

Bartoszek, Wojciech. "On asymptotic cyclicity of doubly stochastic operators." Annales Polonici Mathematici 72.2 (1999): 145-152. <http://eudml.org/doc/262591>.

@article{Bartoszek1999,
abstract = {It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports. If moreover P is Frobenius-Perron or Harris then it is strongly asymptotically cyclic.},
author = {Bartoszek, Wojciech},
journal = {Annales Polonici Mathematici},
keywords = {mixing; doubly stochastic operator; asymptotic stability; Markov operator; asymptotic cyclocity; doubly stochastic operators; weakly asymptotically cyclic; almost overlapping support},
language = {eng},
number = {2},
pages = {145-152},
title = {On asymptotic cyclicity of doubly stochastic operators},
url = {http://eudml.org/doc/262591},
volume = {72},
year = {1999},
}

TY - JOUR
AU - Bartoszek, Wojciech
TI - On asymptotic cyclicity of doubly stochastic operators
JO - Annales Polonici Mathematici
PY - 1999
VL - 72
IS - 2
SP - 145
EP - 152
AB - It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports. If moreover P is Frobenius-Perron or Harris then it is strongly asymptotically cyclic.
LA - eng
KW - mixing; doubly stochastic operator; asymptotic stability; Markov operator; asymptotic cyclocity; doubly stochastic operators; weakly asymptotically cyclic; almost overlapping support
UR - http://eudml.org/doc/262591
ER -

References

top
  1. [B1] W. Bartoszek, Asymptotic stability of iterates of positive contractions on Banach lattices, in: Proc. Int. Conf. Function Spaces (Poznań, 1986), Teubner Texte zur Math. 103, Teubner, 1986, 153-157. 
  2. [B2] W. Bartoszek, Asymptotic periodicity of the iterates of positive contractions on Banach lattices, Studia Math. 91 (1988), 179-188. Zbl0675.47025
  3. [B3] W. Bartoszek, Asymptotic properties of the iterates of stochastic operators on (AL) Banach lattices, Ann. Polon. Math. 52 (1990), 165-173. Zbl0719.47022
  4. [BB] W. Bartoszek and T. Brown, On Frobenius-Perron operators which overlap supports, Bull. Polish Acad. Sci. Math. 45 (1997), 17-24. Zbl0891.47006
  5. [Br] J. R. Brown, Ergodic Theory and Topological Dynamics, Academic Press, New York, 1976. 
  6. [F] S. R. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Reinhold, New York, 1969. 
  7. [K1] J. Komornik, Asymptotic periodicity of the iterates of Markov operators, Tôhoku Math. J. 38 (1986), 15-27. Zbl0578.47020
  8. [K2] J. Komornik, Asymptotic decomposition of Markov operators, Bull. Polish Acad. Sci. Math. 35 (1987), 321-327. Zbl0642.47026
  9. [KL] U. Krengel and M. Lin, On the deterministic and asymptotic σ-algebras of a Markov operator, Canad. Math. Bull. 32 (1989), 64-73. Zbl0638.60079
  10. [L] A. Lasota, Invariant principle for discrete time dynamical systems, Univ. Iagel. Acta Math. 31 (1994), 111-127. Zbl0830.58018
  11. [LM] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Springer, New York, 1993. 
  12. [R1] R. Rudnicki, On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math. 43 (1995), 245-262. Zbl0838.47040
  13. [R2] R. Rudnicki, Asymptotic stability of Markov operators: a counter-example, ibid. 45 (1997), 1-5. 
  14. [Z] R. Zaharapol, Strongly asymptotically stable Frobenius-Perron operators, preprint, 1997. 

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.