On Convergence to Stochastic Integrals

TL;DR

This paper establishes the weak convergence of various functionals of partial sums of causal processes to stochastic integrals, advancing the theoretical understanding of dependent random variables in statistics.

Contribution

It introduces a new method based on Jacod and Shiryaev (2003) to prove weak convergence for functionals of dependent processes.

Findings

Weak convergence of functionals of partial sums of causal processes to stochastic integrals.

Application of a novel method for dependent processes.

Enhancement of theoretical tools in modern statistical analysis.

Abstract

Weak convergence of various general functionals of partial sums of dependent random variables to stochastic integral now play a major role in the modern statistics theory. In this paper, we obtain the weak convergence of various general functionals of partial sums of casual process by means of the method which was introduced in Jacod and Shiryaev (2003).