Asymptotic properties of solutions for impulsive neutral stochastic functional integro-differential equations. (English) Zbl 1469.45011
The authors investigate existence, uniqueness, global attracting sets, quasi-invariant sets, and stability of the mild solutions of the following impulsive neutral stochastic integro-differential equation with finite delay:
\[
d( x(t) + g(t,x_t)) = A( x(t) + g(t,x_t))dt
\]
\[
+ \Big[ \int_0^t \gamma (t-s) (x(t) + g(t,x_t))ds + f(t,x_t) \Big]dt + h(t,x_t)dW(t)
\]
with
\(t \geq 0, t \neq t_k \),
\(
\Delta x(t_k) = x(t_k^+) - x(t_k^-) = I_k(x(t_k^-)), k=1,2,\dots,\)
and \(x_0 = \phi \in PC_{\mathcal{F}_o}^b([-\tau,0];X) \).
Reviewer: Nikolaos Halidias (Athína)
MSC:
| 45M05 | Asymptotics of solutions to integral equations |
| 45M10 | Stability theory for integral equations |
| 45K05 | Integro-partial differential equations |
| 45R05 | Random integral equations |
| 60H20 | Stochastic integral equations |
Keywords:
asymptotic properties of solutions; impulsive neutral stochastic functional integro-differential equation; fixed point principleReferences:
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