Convergence of iterates of Lasota-Mackey-Tyrcha operators

• Autorzy: Wojciech Bartoszek
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

stochastic (Markov) operator; strong Feller kernel; stationary density; asymptotic periodicity

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 60J05: Discrete-time Markov processes on general state spaces
• 47G10: Integral operators
• 47B65: Positive operators and order-bounded operators
• 45D05: Volterra integral equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 63
• Numer: 3
• Strony: 281-292

Daty

wydano

1996

otrzymano

1994-11-20

poprawiono

1995-04-26

Twórcy

autor

Wojciech Bartoszek

• Department of Mathematics, University of South Africa, P.O. Box 392, Pretoria 0001, South Africa

Bibliografia

• [1] K. Baron and A. Lasota, Asymptotic properties of Markov operators defined by Volterra type integrals, Ann. Polon. Math. 57 (1993), 161-175.
• [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] W. Bartoszek, Asymptotic periodicity of the iterates of positive contractions on Banach lattices, Studia Math. 91 (1988), 179-188.
• [4] W. Bartoszek, Asymptotic properties of the iterates of stochastic operators on (AL) Banach lattices, Ann. Polon. Math. 52 (1990), 165-173.
• [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.
• [6] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer, New York, 1993.
• [7] A. Lasota, M. C. Mackey and J. Tyrcha, The statistical dynamics of recurrent biological events, J. Math. Biology 30 (1992), 775-800.
• [8] S. Łojasiewicz, An Introduction to the Theory of Real Functions, Wiley, Chichester, 1988.
• [9] F. Räbiger, Attractors and asymptotic periodicity of positive operators on Banach lattices, Tübingen Ber. Funktionanal. 3 (1993/94), 184-203.
• [10] D. Revuz, Markov Chains, Elsevier, Amsterdam, 1984.
• [11] H. H. Schaefer, Banach Lattices and Positive Operators, Springer, New York, 1974.