Stable convergence in law in approximation of stochastic integrals with respect to diffusions.

We assume that the one-dimensional difiusion X satisffes a stochastic differential equation of the form: dXt = õ(Xt)dt + ö(Xt)=Wt, X0 = x0, t ≥ 0. Let (Xiùn; 0 ≥ i ≥ n) be discrete observations along a fixed time interval [0; T]. We prove that random vectors whose j-th component is p1 ....converge stably in law to a mixed normal random vector with a covariance matrix which depends on the path (Xt; 0 ≥ t ≥ T), when n ! 1. We use this result to prove stable convergence in law for ...)). [ABSTRACT FROM AUTHOR]