On Convergence to Stochastic Integrals

Weak convergence of various general functionals of partial sums of dependent random variables to stochastic integrals now plays a major role in modern statistics theory. In this paper, we obtain the weak convergence of various general functionals of partial sums of causal process by means of the method which was introduced in Jacod and Shiryaev (Limit theorems for stochastic processes. Springer, Berlin, 2003).