Convergence of Probability Measures

TL;DR: In this article, the authors studied the local behavior of empirical processes for independent identically distributed random variables on the real line and obtained best rates of convergence for various types of density estimators as well as error estimates for the Bahadur representation of the quantile process.

TL;DR: For sequences of stochastic integral K ≥ 0, this article showed that functional limit theorem holds under simple natural conditions, and showed that the functional limit Theorem holds for K ≥ 1.

TL;DR: In this paper, the authors illustrate the "martingale method" for proving many-server heavy-traffic stochastic process limits for queueing models, supporting diffusion-process approximations.

TL;DR: This work studies the impact of measurement uncertainty, flow arrival, departure dynamics, and of estimation memory on the performance of a generic MBAC system in a common analytical framework, and shows that a certainty equivalence assumption can grossly compromise the target performance of the system.