Markov operators: applications to diffusion processes and population dynamics

• Autorzy: Ryszard Rudnicki
• Języki publikacji: EN

Abstrakty

EN

This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.

Słowa kluczowe

EN

Markov operator; asymptotic stability; diffusion process; partial differential equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2000
• Tom: 27
• Numer: 1
• Strony: 67-79

Daty

wydano

2000

otrzymano

1999-01-15

Twórcy

autor

Ryszard Rudnicki

• Institute of Mathematics, Polish Academy of Sciences, Staromiejska 8/6 40-013 Katowice, Poland

Bibliografia

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• [6] O. Diekmann, H. J. A. Heijmans and H. R. Thieme, On the stability of the cell size distribution, J. Math. Biol. 19 (1984), 227-248.
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• [10] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise. Stochastic Aspects of Dynamics, Appl. Math. Sci. 97, Springer, New York, 1994.
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• [14] J. Malczak, An application of Markov operators in differential and integral equations, Rend. Sem. Mat. Univ. Padova 87 (1992), 281-297.
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• [16] K. Pichór, Asymptotic stability of a partial differential equation with an integral perturbation, Ann. Polon. Math. 68 (1998), 83-96,
• [17] K. Pichór and R. Rudnicki, Stability of Markov semigroups and applications to parabolic systems, J. Math. Anal. Appl. 215 (1997), 56-74.
• [18] K. Pichór and R. Rudnicki, Asymptotic behaviour of Markov semigroups and applications to transport equations, Bull. Polish Acad. Sci. Math. 45 (1997), 379-397.
• [19] R. Rudnicki, Asymptotic behaviour of a transport equation, Ann. Polon. Math. 57 (1992), 45-55.
• [20] R. Rudnicki, Asymptotic behaviour of an integro-parabolic equation, Bull. Polish Acad. Sci. Math. 40 (1992), 111-128.
• [21] R. Rudnicki, Asymptotic properties of the Fokker-Planck equation, in: Chaos--The Interplay between Stochastics and Deterministic Behaviour, Karpacz '95 Proc., P. Garbaczewski, M. Wolf and A. Weron (eds.), Lecture Notes in Phys. 457, Springer, Berlin, 1995, 517-521.
• [22] R. Rudnicki, On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math. 43 (1995), 245-262.
• [23] R. Rudnicki, Asymptotic stability of Markov operators: a counter-example, ibid. 45 (1997), 1-5.
• [24] R. Rudnicki and K. Pichór, Markov semigroups and stability of the cell maturity distribution, J. Biol. Systems, submitted.
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• [27] J. J. Tyson and K. B. Hannsgen, Cell growth and division: A deterministic/probabilistic model of the cell cycle, ibid. 23 (1986), 231-246.