bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Horbacz, Katarzyna:
Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations
Bollettino dell'Unione Matematica Italiana Serie 8 9-B (2006), fasc. n.3, p. 545-566, (english)
pdf (494 Kb), djvu (192 Kb). | MR 2274111 | Zbl 1177.60058

Sunto

Si considera l'equazione differenziale stocastica del tipo \begin{equation}\tag{1}dX(t) = a(X(t); \xi(t)) \, dt + \int_\Theta b(X(t); \theta) \mathcal{N}_p(dt; d\theta)\end{equation} per $t \geq 0$ con condizione iniziale $X(0) = x_0$. Diamo condizioni sufficienti per la stabilità delle soluzioni che generano il semigruppo degli operatori di Markov.
Referenze Bibliografiche
[1] O.L.V. COSTA, Stationary distributions for piecewise-deterministic Markov processes, J. Appl. Prob., 27 (1990), 60-73. | Zbl 0703.60068
[2] M.H.A. DAVIS, Piecewise-deterministic Markov processes : A general class of nondiffusion stochastic models, J. R. Statist. Soc. B (1984, 46), 353-388. | Zbl 0565.60070
[3] M.H.A. DAVIS, Markov Models and Optimization, Chapman and Hall, London (1993). | Zbl 0780.60002
[4] O. DIEKMANN - H.J.A.M. HEIJMANS - H.R. THIEME, On the stability of the cell size distribution, J. Math. Biol., 19 (1984), 227-248. | Zbl 0543.92021
[5] R. FORTET - B. MOURIER, Convergence de la répartition empirique vers la répartition théorétique, Ann. Sci. École. Norm. Sup., 70 (1953), 267-285. | fulltext EuDML | Zbl 0053.09601
[6] U. FRISCH, Wave propagation in random media, Probabilistic Methods in Applied Mathematics ed. A.T. Bharucha - Reid, Academic Press 1968.
[7] K. HORBACZ, Randomly connected dynamical systems - asymptotic stability, Ann. Polon. Math., 68.1 (1998), 31-50. | fulltext EuDML | Zbl 0910.47003
[8] K. HORBACZ, Invariant measures related with randomly connected Poisson driven diferential equations, Ann. Polon. Math., 79.1 (2002), 31-44. | fulltext EuDML | Zbl 1011.60036
[9] K. HORBACZ, Randomly connected differential equations with Poisson type perturbations, Nonlinear Studies, 9.1 (2002), 81-98.
[10] K. HORBACZ, Random dynamical systems with jumps, J. Appl. Prob., 41 (2004), 890-910. | Zbl 1091.47012
[11] K. HORBACZ, J. MYJAK - T. SZAREK, Stability of random dynamical system on Banach spaces, (to appear). | Zbl 1121.37037
[12] J.B. KELLER, Stochastic equations and wave propagation in random media, Proc. Symp. Appl. Math., 16 (1964), 1456-1470.
[13] A. LASOTA - M.C. MACKEY, Chaos, Fractals and Noise - Stochastic Aspect of Dynamics, Springer-Verlag New York (1994).
[14] A. LASOTA - J. TRAPLE, Invariant measures related with Poisson driven stochastic differential equation, Stoch. Proc. and Their Appl. 106.1 (2003), 81-93. | Zbl 1075.60535
[15] A. LASOTA - J.A. YORKE, Lower bound technique for Markov operators and iterated function systems, Random and Computational Dynamics, 2 (1994), 41-77. | Zbl 0804.47033
[16] S. MEYN and R TWEEDIE, Markov Chains and Stochastic Stability, Springer-Verlag Berlin 1993.
[17] J. TRAPLE, Markov semigroup generated by Poisson driven differential equations, Bull. Pol. Ac. Math., 44 (1996), 161-182. | Zbl 0861.45008

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali