This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.
This paper discusses the problem of testing the sphericity of population covariance matrix when the sample size n and the dimensionality p both tend to infinity with p / n → c ∈ (0,1). A new test statistic is presented by utilizing an inequality, and asymptotic properties of the proposed statistic are derived for generally distributed population under the null hypothesis. Numerical simulations demonstrate that the proposed statistic has a significant improvement on test powers under the alternative hypothesis by comparing with some congeneric statistics.
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