Stability of Markov semigroups and applications to parabolic systems

Journal of Mathematical Analysis and Applications

Volumn 215, Issue 1, 1997, Pages 56-74

  Pichór, Katarzyna ^a   Rudnicki, Ryszard ^a,b  

^a UNIVERSITY OF SILESIA   (Poland)

^b INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; MARKOV PROCESSES; THEOREM PROVING;

MARKOV SEMIGROUPS; PARABOLIC SYSTEMS; TWO STATE DIFFUSION PROCESSES;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0031260781     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5609     Document Type: Article

References (24)

1. Balakrishnan V., Van den Broeck C., Hanggi P. First-passage times of non-Markovian processes: the case of a reflecting boundary. Phys. Rev. A. 38:1988;4213-4222.
2. Baron K., Lasota A. Asymptotic properties of Markov operators defined by Volterra type integrals. Ann. Polon. Math. 57:1993;161-175.
3. Bezak V. A modification of the Wiener process due to a Poisson random train of diffusion-enhancing pulses. J. Phys. A. 25:1992;6027-6041.
4. S. Chandrasekhar, G. Münch, The theory of fluctuations in brightness of the Milky-Way, Astrophys. J. 125, 94, 123.
5. DlŁotko T., Lasota A. Statistical stability and the lower bound function technique. Brezis H., Crandall M., Kappel F. Semigroups Theory and Applications. 1987;75-95 Longman Scientific and Technical.
6. Dunford N., Schwartz J. T. Linear Operators. 1968;Interscience, New York.
7. Feller W. The parabolic differential equations and the associated semi-groups of transformations. Ann. of Math. 55:1952;468-519.
8. The Ergodic Theory of Markov Processes. 1969;Van Nostrand-Reinhold, New York.
9. Hasminskii R. Z. Ergodic properties of recurrent diffusion processes and stabilization of the solutions of the Cauchy problem for parabolic equations. Teor. Veroyatnost. i Primenen. 5:1960;196-214.
10. Hille E. On the integration problem for Fokker-Planck's equation. 10th Congress of Scandinavian Mathematics. 1950;Trondheim.
11. Komorowski T., Tyrcha J. Asymptotic properties of some Markov operators. Bull. Polish Acad. Math Sci. 37:1989;221-228.
12. Lasota A., Mackey M. C. Chaos, Fractals and Noise. Stochastic Aspects of Dynamics. Springer Applied Mathematical Sciences. 97:1994;Springer-Verlag, New York.
13. LŁuczka J., Rudnicki R. Randomly flashing diffusion: asymptotic properties. J. Statist. Phys. 83:1996;1149-1164.
14. Mackey M. C., Rudnicki R. Global stability in a delayed partial differential equation describing cellular replication. J. Math. Biol. 33:1994;89-109.
15. Malczak J. An application of Markov operators in differential and integral equations. Rend. Sem. Mat. Univ. Padova. 87:1992;281-297.
16. Metz J. A. J., Diekmann O. The Dynamics of Physiologically Structured Populations. Springer Lecture Notes in Biomathematics. 68:1986;Springer-Verlag, New York.
17. Rudnicki R. Asymptotic behaviour of a transport equation. Ann. Polon. Math. 57:1992;45-55.
18. Rudnicki R. Asymptotic behaviour of an integro-parabolic equation. Bull. Polish Acad. Sci. Math. 40:1992;111-128.
19. 1. J. Differential Equations. 102:1993;391-401.
20. Rudnicki R. Asymptotic properties of the Fokker-Planck equation. Garbaczewski P., Wolf M., Weron A. Chaos - The Interplay between Stochastics and Deterministic Behaviour. Lecture Notes in Physics. 457:1995;517-521 Springer-Verlag, Berlin.
21. Rudnicki R. On asymptotic stability and sweeping for Markov operators. Bull. Polish Acad. Sci. Math. 43:1995;245-262.
22. 1. J. Math. Anal. Appl. 112:1985;335-346.
23. Traple J. Markov semigroups generated by Poisson driven differential equations. Bull. Polish. Acad. Sci. Math. 44:1996;230-252.
24. Yosida K. An operator-theoretical treatment of temporally, homogeneous Markoff process. J. Math. Soc. Japan. 1:1949;244-253.