Asymptotic properties of Markov operators defined by Volterra type integrals

Karol Baron; Andrzej Lasota

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 2, page 161-175
  • ISSN: 0066-2216

Abstract

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New sufficient conditions for asymptotic stability of Markov operators are given. These criteria are applied to a class of Volterra type integral operators with advanced argument.

How to cite

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Karol Baron, and Andrzej Lasota. "Asymptotic properties of Markov operators defined by Volterra type integrals." Annales Polonici Mathematici 58.2 (1993): 161-175. <http://eudml.org/doc/262424>.

@article{KarolBaron1993,
abstract = {New sufficient conditions for asymptotic stability of Markov operators are given. These criteria are applied to a class of Volterra type integral operators with advanced argument.},
author = {Karol Baron, Andrzej Lasota},
journal = {Annales Polonici Mathematici},
keywords = {Markov operator; integral Markov operator; stationary density; asymptotic stability; sweeping; asymptotic stability of Markov operators; Volterra type integral operators},
language = {eng},
number = {2},
pages = {161-175},
title = {Asymptotic properties of Markov operators defined by Volterra type integrals},
url = {http://eudml.org/doc/262424},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Karol Baron
AU - Andrzej Lasota
TI - Asymptotic properties of Markov operators defined by Volterra type integrals
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 2
SP - 161
EP - 175
AB - New sufficient conditions for asymptotic stability of Markov operators are given. These criteria are applied to a class of Volterra type integral operators with advanced argument.
LA - eng
KW - Markov operator; integral Markov operator; stationary density; asymptotic stability; sweeping; asymptotic stability of Markov operators; Volterra type integral operators
UR - http://eudml.org/doc/262424
ER -

References

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  1. [1] S. R. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Math. Stud. 21, Van Nostrand, 1969. 
  2. [2] H. Gacki and A. Lasota, Markov operators defined by Volterra type integrals with advanced argument, Ann. Polon. Math. 51 (1990), 155-166. Zbl0721.34094
  3. [3] T. Komorowski and J. Tyrcha, Asymptotic properties of some Markov operators, Bull. Polish Acad. Sci. Math. 37 (1989), 221-228. Zbl0767.47012
  4. [4] U. Krengel, Ergodic Theorems, de Gruyter, 1985. 
  5. [5] A. Lasota and M. C. Mackey, Globally asymptotic properties of proliferating cell populations, J. Math. Biol. 19 (1984), 43-62. Zbl0529.92011
  6. [6] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge University Press, 1985. Zbl0606.58002
  7. [7] A. Lasota, M. C. Mackey and J. Tyrcha, The statistical dynamics of recurrent biological events, J. Math. Biol. 30 (1992), 775-800. Zbl0763.92001
  8. [8] J. Malczak, An application of Markov operators in differential and integral equations, Rend. Sem. Mat. Univ. Padova, in press. Zbl0795.60071
  9. [9] J. Socała, On the existence of invariant densities for Markov operators, Ann. Polon. Math. 48 (1988), 51-56. Zbl0657.60089
  10. [10] J. Tyrcha, Asymptotic stability in a generalized probabilistic/deterministic model of the cell cycle, J. Math. Biol. 26 (1988), 465-475. Zbl0716.92017
  11. [11] J. J. Tyson and K. B. Hannsgen, Global asymptotic stability of the size distribution in probabilistic model of the cell cycle, J. Math. Biol. 22 (1985), 61-68. Zbl0558.92012
  12. [12] J. J. Tyson and K. B. Hannsgen, Cell growth and division: A deterministic/probabilistic model of the cell cycle, J. Math. Biol. 23 (1986), 231-246. Zbl0582.92020

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