ArticleOriginal scientific text

Title

Asymptotic properties of Markov operators defined by Volterra type integrals

Authors 1, 1

Affiliations

  1. Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

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.

Keywords

Markov operator, integral Markov operator, stationary density, asymptotic stability, sweeping

Bibliography

  1. S. R. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Math. Stud. 21, Van Nostrand, 1969.
  2. H. Gacki and A. Lasota, Markov operators defined by Volterra type integrals with advanced argument, Ann. Polon. Math. 51 (1990), 155-166.
  3. T. Komorowski and J. Tyrcha, Asymptotic properties of some Markov operators, Bull. Polish Acad. Sci. Math. 37 (1989), 221-228.
  4. U. Krengel, Ergodic Theorems, de Gruyter, 1985.
  5. A. Lasota and M. C. Mackey, Globally asymptotic properties of proliferating cell populations, J. Math. Biol. 19 (1984), 43-62.
  6. A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge University Press, 1985.
  7. A. Lasota, M. C. Mackey and J. Tyrcha, The statistical dynamics of recurrent biological events, J. Math. Biol. 30 (1992), 775-800.
  8. J. Malczak, An application of Markov operators in differential and integral equations, Rend. Sem. Mat. Univ. Padova, in press.
  9. J. Socała, On the existence of invariant densities for Markov operators, Ann. Polon. Math. 48 (1988), 51-56.
  10. J. Tyrcha, Asymptotic stability in a generalized probabilistic/deterministic model of the cell cycle, J. Math. Biol. 26 (1988), 465-475.
  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.
  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.
Pages:
161-175
Main language of publication
English
Received
1992-07-02
Published
1993
Exact and natural sciences