Asymptotic stability of empirical processes and related functionals (Q2633763)

Let $\xi_1,\xi_2,\dots$ be a stationary sequence of random trials, with $m_n$ the empirical measure of the first $n$ of these trials. One of the main results of the present paper is the almost sure convergence of these empirical measures in the $\psi$-weak topology as $n\rightarrow\infty$, where $\psi$ is a continuous function playing the role of a gauge function and the limit is in terms of a certain conditional distribution. \par Motivated by applications in financial risk, the authors also consider a functional $\tau$, studying strong consistency of the statistics $\tau(m_n)$ and giving conditions for asymptotic stability of $\tau(m_n)$ with respect to given perturbations of the data.