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This paper is concerned with a class of impulsive stochastic partial integrodifferential equations (ISPIEs) with delays and Poisson jumps. First, using the resolvent operator technique and contraction mapping principle, we can directly prove the existence and uniqueness of the mild solution for the system mentioned above. Then we develop a new impulsive integral inequality to obtain the global, both pth moment exponential stability and almost surely exponential stability of the mild solution is established with sufficient conditions. Also, a numerical example is provided to validate the theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of Sobolev-type stochastic differential equations driven by G-Brownian motion (G-SSDEs, in short). We prove the existence and uniqueness of the mild solution for G-SSDEs. By means of two integral inequalities, the attracting and quasi-invariant sets of the equations are obtained. As a byproduct, the exponentially stability of the solution in mean-square sense is derived. An example is given to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper aims at analyzing the quasi-invariant and attractive sets for a class of inertial neural networks with time-varying and infinite distributed delays. By utilizing the properties of nonnegative matrix, a new bidirectional-like delay integral inequality is developed. Some sufficient conditions are obtained for the existence of the quasi-invariant and attractive sets of the discussed system according to the bidirectional-like integral inequality. Besides, the framework of the quasi-invariant and attractive sets for the concerned system is provided. Finally, one example is analyzed to clarify the validity of our results. [ABSTRACT FROM AUTHOR]

In this article, we investigate a class of neutral stochastic partial functional integrodifferential equations with impulsive effects. The results are obtained by using the new integral inequalities, the attracting and quasi-invariant sets combined with theories of resolvent operators. In the end, one example is given to illustrate the feasibility and effectiveness of results obtained. [ABSTRACT FROM AUTHOR]

Abstract The paper is devoted to investigating a class of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion. By establishing two new impulsive integral inequalities which improve the inequalities established by Li (Neurocomputing 177:620-627, 2016) and Long et al. (Stat. Probab. Lett. 82(9):1699-1709, 2012), attracting and quasi-invariant sets of the system are obtained. Moreover, exponential stability of the mild solution is established with sufficient conditions.

The paper is devoted to investigating a class of neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion. By establishing two new impulsive integral inequalities which improve the inequalities established by Li (Neurocomputing 177:620-627, 2016) and Long et al. (Stat. Probab. Lett. 82(9):1699-1709, 2012), attracting and quasi-invariant sets of the system are obtained. Moreover, exponential stability of the mild solution is established with sufficient conditions. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a class of impulsive neutral stochastic functional differential equations driven by fractional Brownian motion in the Hilbert space. We obtain the global attracting and quasi-invariant sets of this kind of equations driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 / 2 , 1 ) . Especially, the sufficient conditions ensuring the exponential p -stability of the mild solution of the considered equations are obtained. In the end, one example is given to illustrate the feasibility and effectiveness of results obtained. [ABSTRACT FROM AUTHOR]

The aim of this article is to study the attracting and quasi-invariant sets for a class of impulsive stochastic difference equations. By establishing a difference inequality, we obtain the attracting and quasi-invariant sets of systems under consideration. An example is given to illustrate the theory. [ABSTRACT FROM AUTHOR]