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Abstrakty
A new sufficient condition for the asymptotic stability of a locally Lipschitzian Markov semigroup acting on the space of signed measures. M[sig] is proved. This criterion is applied to the semigroup of Markov operators generated by a Poisson driven stochastic differential equation.
Wydawca
Rocznik
Tom
Strony
211--222
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland, gacki@ux2.math.us.edu.pl
Bibliografia
- [1] H. Gacki, An application of the Kantorovich-Rubinstein maximum principle in the stability theory of Markov operators, Bull. Polish Acad. Sci. Math. 46 (1998), 215-223.
- [2] J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981), 713-747.
- [3] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
- [4] L. V. Kantorovich and G. S. Rubinstein, On a space of completely additive functions, Vestnik Leningrad Univ. 13 (1958), 52-59 (in Russian).
- [5] A. Lasota, Invariant principle for discrete time dynamical systems, Univ. Iagell. Acta Math. 31 (1994), 111-127.
- [6] -, From fractals to stochastic differential equations, in: Chaos-The Interplay Between Stochastic and Deterministic Behaviour (Karpacz, 1995), P. Garbaczewski et al. (eds.), Lecture Notes in Phys. 457, Springer, Berlin, 1995, 235-255.
- [7] A. Lasota and M. C. Mackey, Chaos, Fractals, and Noise, Springer, Berlin, 1994.
- [8] A. Lasota and J. Traple, An application of the Kantorovich-Rubinstein maximum principle in the theory of the Tjon-Wu equation, J. Differential Equations 159 (1999), 578-596.
- [9] A. Lasota and J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comp. Dyn. 2 (1994), 41-77.
- [10] J. Malczak, Statistical stability of Poisson driven differential equations, Bull. Polish Acad. Sci. Math. 41 (1993), 159-176.
- [11] S. T. Rachev, Probability Metrics and the Stability of Stochastic Models, Wiley, New York, 1991.
- [12] J. Traple, Markov semigroups generated by Poisson driven differential equations, Bull. Polish Acad. Sci. Math. 44 (1996), 160-182.
- [13] -, On the asymptotic stability of Markov semigroups, ibid. 44 (1996), 183-195.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0004-0022