For this paper, we consider the almost sure exponential stability of uncertain stochastic Hopfield neural networks based on subadditive measures. Firstly, deduce two corollaries, using Itô–Liu formula. Then, introduce concept for networks. Next, investigate networks, Lyapunov method, Liu inequality, lemma, and martingale inequality. In addition, prove sufficient conditions stability. Furthermor...

Using key tools such as Itô’s formula for general semimartingales, Kunita’s moment estimates for Lévy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Lévy noise are stable in probability, almost surely and moment exponentially stable. Keywords; stochastic differential equ...

the purpose of this paper is to study the convergence and the almost sure t-stability of the modied 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 resu...

Abstract G-Brownian motion has potential applications in uncertainty problems and risk measures, which attracted the attention of many scholars. This study investigates almost sure exponential stability nonlinear stochastic delay hybrid systems driven by motion. Due to non-linearity G-expectation distribution motion, it is difficult this issue. Firstly, existence global unique solution derived ...

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are deriv...

This work is devoted to stability analysis of numerical solutions for jump diffusions and jump diffusions with Markovian switching. Different from the existing treatment of Euler-Maurayama methods for solutions of stochastic differential equations, we use techniques from stochastic approximation. We analyze the almost sure exponential stability and exponential pstability. Then Markovian regime-...

This paper considers the stability of moments of stochastic systems, such as stability of the mean or mean-square stability. The exponential growth behavior of moments is compared to almost sure exponential growth via Lyapunov exponents. We develop a series of indices that are useful to describe system performance under random perturbations. The theory is applied to two examples, including an e...