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2000 | 84/85 | 1 | 255-263
Tytuł artykułu

Strong and weak stability of some Markov operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An integral Markov operator $P$ appearing in biomathematics is investigated. This operator acts on the space of probabilistic Borel measures. Let $μ$ and $ν$ be probabilistic Borel measures. Sufficient conditions for weak and strong convergence of the sequence $(P^{n}μ-P^{n}ν)$ to $0$ are given.
Rocznik
Tom
Numer
1
Strony
255-263
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-07-27
poprawiono
2000-01-14
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • [1] M. F. Barnsley, Fractals Everywhere, Acad. Press, New York, 1988.
  • [2] K. Baron and A. Lasota, Asymptotic properties of Markov operators defined by Volterra type integrals, Ann. Polon. Math. 58 (1993), 161-175.
  • [3] C. J. K. Batty, Z. Brzeźniak and D. A. Greenfield, A quantitative asymptotic theorem for contraction semigroups with countable unitary spectrum, Studia Math. 121 (1996), 167-183.
  • [4] S. R. Foguel, The Ergodic Theory of Markov Processes, Van Nostrand Reinhold, New York, 1969.
  • [5] S. R. Foguel, Harris operators, Israel J. Math. 33 (1979), 281-309.
  • [6] H. Gacki and A. Lasota, Markov operators defined by Volterra type integrals with advanced argument, Ann. Polon. Math. 51 (1990), 155-166.
  • [7] A. Iwanik, Baire category of mixing for stochastic operators, Rend. Circ. Mat. Palermo (2) Suppl. 28 (1992), 201-217.
  • [8] T. Komorowski and J. Tyrcha, Asymptotic properties of some Markov operators, Bull. Polish Acad. Sci. Math. 37 (1989), 221-228.
  • [9] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise. Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer, New York, 1994.
  • [10] A. Lasota and M. C. Mackey, Global asymptotic properties of proliferating cell populations, J. Math. Biol. 19 (1984), 43-62.
  • [11] A. Lasota, M. C. Mackey and J. Tyrcha, The statistical dynamics of recurrent biological events, ibid. 30 (1992), 775-800.
  • [12] M. Lin, Mixing for Markov operators, Z. Wahrsch. Verw. Gebiete 19 (1971), 231-242.
  • [13] K. Łoskot and R. Rudnicki, Sweeping of some integral operators, Bull. Polish Acad. Sci. Math. 37 (1989), 229-235.
  • [14] J. van Neerven, The Asymptotic Behaviour of a Semigroup of Linear Operators, Birkhäuser, Basel, 1996.
  • [15] E. Nummelin, General Irreducible Markov Chains and Non-Negative Operators, Cambridge Tracts in Math. 83, Cambridge Univ. Press, Cambridge, 1984.
  • [16] R. Rudnicki, Stability in $L^1$ of some integral operators, Integral Equations Operator Theory 24 (1996), 320-327.
  • [17] R. Rudnicki, On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math. 43 (1995), 245-262.
  • [18] J. Tyrcha, Asymptotic stability in a generalized probabilistic/deterministic model of the cell cycle, J. Math. Biol. 26 (1988), 465-475.
  • [19] J. J. Tyson, Mini review: Size control of cell division, J. Theoret. Biol. 120 (1987), 381-391.
  • [20] J. J. Tyson and K. B. Hannsgen, Global asymptotic stability of the size distribution in probabilistic models of the cell cycle, J. Math. Biol. 22 (1985), 61-68.
  • [21] J. J. Tyson and K. B. Hannsgen, Cell growth and division: A deterministic/probabilistic model of the cell cycle, ibid. 23 (1986), 231-246.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv84i1p255bwm
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