Domain of attraction of the normal law Brownian bridge a b s t r a c t domain of attraction of the normal law with mean zero and possibly infinite variance, Q (n) = R(n)/S(n) be the rescaled range statistic, where R(n)

We present a generalization of Zubov’s method to perturbed differential equations. The goal is to characterize the domain of attraction of a set which is uniformly locally asymptotically stable under all admissible time varying perturbations. We show that in this general setting the straightforward generalization of the classical Zubov’s equations has a unique viscosity solution which character...

In this work, we study the asymptotic distribution of the normalized sum of independent, identically distributed random variables under the finite mixture models. In the Theorem we give necessary conditions for a distribution function of a mixed population with k components to belong to the domain of attraction of an α-stable distribution, by assuming that each component of the mixture also per...

We present a method to estimate the domain of attraction of a class of discretetime Lur’e systems. A new notion of LNL-invariance, stronger than the traditional invariance concept, is introduced. An algorithm to determinate the largest LNL-invariant set for this class of systems is proposed. Moreover, it is proven that the LNL-invariant sets provided by this algorithm are polyhedral convex sets...

This paper deals with the stability analysis and anti-windup design of discrete-time systems subject to actuator saturation. We present a new saturationdependent Lyapunov function to estimate the domain of attraction, which is then formulated and solved as a constrained LMI optimization problem. Further we propose an anti-windup compensation method to enlarge the domain of attraction in the pre...