The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

In this paper, we study a new type of stochastic functional differential equations which are called hybrid pantograph (HPSFDEs). We investigate moment properties and sample the solutions such as exponential stability, almost sure stability polynomial stability. Moreover, several theoretical examples one practical example given to illustrate our theory.

The exponential stability, in both mean square and almost sure senses, for energy solutions to a nonlinear and non-autonomous stochastic PDEs with finite memory is investigated. Various criteria for stability are obtained. An example is presented to demonstrate the main results.

Uncertain differential equation is a type of differential equation driven by Liu process. So far, concepts of stability and stability in mean for uncertain differential equations have been proposed. This paper aims at providing a concept of almost sure stability for uncertain differential equation. A sufficient condition is given for an uncertain differential equation being almost surely stable...

The problem of the stability of a class of stochastic linear hybrid systems with a special structure of matrices and a multiplicative excitation is considered. Sufficient conditions of the exponential p-th mean stability and the almost sure stability for a class of stochastic linear hybrid systems with the Markovian switching are derived. Also, sufficient conditions of the exponential mean-squa...