Geodesic
Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 545-566

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We consider the stochastic differential equation \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} for $t \geq 0$ with the initial condition $X(0) = x_{0}$. We give sufficient conditions for the asymptotic stability of the semigroup $\{P^{t}\}_{t \geq 0}$ generated by the stochastic differential equation (1). 
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     author = {Horbacz, Katarzyna},
     title = {Asymptotic stability of a semigroup generated by randomly connected {Poisson} driven differential equations},
     journal = {Bollettino della Unione matematica italiana},
     pages = {545--566},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {3},
     year = {2006},
     zbl = {1177.60058},
     mrnumber = {2274111},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a1/}
}
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Horbacz, Katarzyna. Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 545-566. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a1/