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
Con il contributo del Ministero per i Beni e le Attività Culturali