Abstract
In many recent applications, statistics are under the form of discrete stochastic integrals integral X-n(t)dY(n)(t), where X-n(t) and Y-n(t), are two processes over some subset of reals. In this work, we establish a basic theorem on the convergence in distribution of a sequence of discrete stochastic integrals relative to two weighted sums of a L-2-mixing process. This result extends earlier corresponding theorems in Chan & Wei (1988) and in Truong-van & Larramendy (1996). Its proof is based on the classical martingale approximation technique, and from a derivation of Kurtz & Protter's theorem (1991) on the convergence in distribution of sequences of Ito stochastic integrals relative to two semi-martingales. Furthermore, various applications to asymptotic statistics are also given, mainly those concerning least squares estimators for integrated GARCH models.