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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• [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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• [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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