Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations

Katarzyna Horbacz

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 3, page 545-566
  • ISSN: 0392-4041

Abstract

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We consider the stochastic differential equation d ⁢ X ⁢ ( t ) = a ⁢ ( X ⁢ ( t ) ; ξ ⁢ ( t ) ) ⁢ d ⁢ t + ∫ Θ b ⁢ ( X ⁢ ( t ) ; θ ) ⁢ 𝒩 p ⁢ ( d ⁢ t ; d ⁢ θ ) for t ≥ 0 with the initial condition X ⁢ ( 0 ) = x 0 . We give sufficient conditions for the asymptotic stability of the semigroup { P t } t ≥ 0 generated by the stochastic differential equation (1).

How to cite

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Horbacz, Katarzyna. "Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations." Bollettino dell'Unione Matematica Italiana 9-B.3 (2006): 545-566. <http://eudml.org/doc/289608>.

@article{Horbacz2006,
abstract = {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).},
author = {Horbacz, Katarzyna},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {545-566},
publisher = {Unione Matematica Italiana},
title = {Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations},
url = {http://eudml.org/doc/289608},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Horbacz, Katarzyna
TI - Asymptotic stability of a semigroup generated by randomly connected Poisson driven differential equations
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/10//
PB - Unione Matematica Italiana
VL - 9-B
IS - 3
SP - 545
EP - 566
AB - 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).
LA - eng
UR - http://eudml.org/doc/289608
ER -

References

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  13. LASOTA, A. - MACKEY, M.C., Chaos, Fractals and Noise - Stochastic Aspect of Dynamics, Springer-VerlagNew York (1994). 
  14. LASOTA, A. - TRAPLE, J., Invariant measures related with Poisson driven stochastic differential equation, Stoch. Proc. and Their Appl.106.1 (2003), 81-93. Zbl1075.60535
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