This paper mainly deals with the almost surely exponential stability and exponential p-th moment stability for a class of stochastic Cohen–Grossberg neural networks with distributed delays and reaction–diffusion term. By constructing suitable Lyapunov functional, employing the nonnegative semi-martingale convergence theorem and applying matrix theory and stochastic analysis technique, two delay...

The authors in their papers (Liao and Mao, Stochast. Anal. Appl. 14 (2) (1996a) 165–185; Neural, Parallel Sci. Comput. 4 (2) (1996b) 205–244) initiated the study of stability and instability of stochastic neural networks and this paper is the continuation of their research in this area. The main aim of this paper is to discuss almost sure exponential stability for a stochastic delay neural netw...

For a large class of expanding maps of the interval, we prove that partial sums of Lipschitz observables satisfy an almost sure central limit theorem (ASCLT). In fact, we provide a speed of convergence in the Kantorovich metric. Maxima of partial sums are also shown to obey an ASCLT. The key-tool is an exponential inequality recently obtained. Then we derive almost-sure convergence rates for th...

In this paper, we study the convergence and almost sure (S, T)−stability of Jungck-Noor type, Jungck-SP type, Jungck-Ishikawa type and Jungck-Mann type random iterative algorithms for some kind of a general contractive type random operators (2.14) in a separable Banach spaces. The Bochner integrability of random fixed point of this kind of random operators, the convergence and almost sure (S, T...

So far, a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability. This paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean-square sense. The results are expressed in terms of linear matrix inequalities (LMIs) which are easy to ...

⎯In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improv...

We study random perturbations of quasi-periodic uniformly discrete sets in the d-dimensional euclidean space. By means Diffraction Theory, we find conditions under which a set X can be almost surely recovered from its perturbations. This extends recent periodic case result Yakir (Int Math Res Notices 1–19, 2020).

Two counterexamples, addressing questions raised in Adamczak (2019) and Poly Zheng (2019), are provided. Both counterexamples related to chaoses. Let F n = Y + Z , where the random variables belong different chaoses of uniformly bounded degree. It may be that ? a . s 0 L 2 ? E { sup | } < ? for some > yet fails converge a.s.