Convergence to Stochastic Integrals with Non-linear integrands. by Caceres, C, Nielsen, B

“…In this paper we present a general result concerning the convergence to stochastic integrals with non-linear integrands. The key finding represents a generalization of Chan and Wei's (1988) Theorem 2.4 and that of Ibragimov and Phillips' (2004) Theorem 8.2. …”

A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales. by Barndorff-Nielsen, O, Graversen, S, Jacod, J, Podolskij, M, Shephard, N

“…If further is a possibly discontinuous semimartingale driven by a Brownian motion which may be correlated with W and by a Poisson random measure, we prove a central limit theorem, in the sense that \sqrt(n) (V(Y;r,s)^n-V(Y;r,s)) converges in law to a process which is the stochastic integral with respect to some other Brownian motion W', which is independent of the driving terms of Y and \sigma. …”

Test for cointegration rank in general vector autoregressions. by Nielsen, B

“…To prove the results the convergence of stochastic integrals with respect to singular explosive processes is considered.…”