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The pointwise dimension for invariant measures related with Poisson driven stochastic differential equations

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Języki publikacji
EN
Abstrakty
EN
Sufficient conditions for the asymptotic stability of Poisson driven stochastic differential equations on a separable Banach space are presented. It is also proved that the lower pointwise dimension of a unique invariant measure is greater than or equal to log 2/ log 3.
Rocznik
Strony
241--250
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
  • Dipartimento di Matematica Pura ed Applicata, Universitá di L’aquila, Via Vetoio, 67100 L’aquila, Italy
Bibliografia
  • [1] R. M. Dudley, Probabilities and metrics, Arhus Universitet, Arhus 1976.
  • [2] R. Fortet, B. Mourier, Convergence de la répartition empirique vers la répartition théorétique Ann. Sci. École Norm. Sup., 70 (1953) 267-285.
  • [3] I. I. Gihman, A. Y. Skorohod, Stochastic differential equations and their applications (in Russian), Naukova Dumka, Kiev 1982.
  • [4] N. Ikeda, S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland, Amsterdam 1981.
  • [5] A. Lasota, From fractals to stochastic differential equations, in: Chaos – The Interplay Between Stochastic and Deterministic Behaviour (Karpacz 1995); Proceedings of the XXXIst Winter School of Theoretical Physics, eds.: P. Garbaczewski, M. Wolf, A. Weron, Lecture Notes in Phys., Springer-Verlag, Berlin (1995) 235-255.
  • [6] A. Lasota, J. Myjak, On a dimension of measures, Bull. Pol. Ac.: Math., this issue, pp. 221-235.
  • [7] A. Lasota, J. Traple, Invariant measures related with Poisson driven stochastic differential equation, to be published.
  • [8] A. Lasota, J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynam., 2 (1994) 41-77.
  • [9] T. Szarek, The stability of Markov operators on Polish spaces, Studia Math., 143 (2000) 145-152.
  • [10] T. Szarek, S. Wędrychowicz, Markov semigroups generated by a Poisson driven differential equation, Nonlinear Anal., 50 (1) (2002) 41-54.
  • [11] J. Traple, Markov semigroups generated by Poisson driven differential equations, Bull. Pol. Ac.: Math., 44 (1996) 161-182.
  • [12] L.-S. Young, Dimension, entropy and Lyapunov exponents, Ergodic Theory Dynam. Systems, (1982) 109-124.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT2-0001-1321
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