Approximations of a complex Brownian motion with processes constructed from a process with independent increments

TL;DR

This paper demonstrates how complex Brownian motion can be approximated by processes derived from independent increment processes, providing conditions for such approximations and extending results to multidimensional cases.

Contribution

It introduces new approximation methods for complex Brownian motion using processes with independent increments, including Le9vy processes and multidimensional extensions.

Findings

Established sufficient conditions for approximation validity.

Applied results specifically to Le9vy processes.

Extended approximation techniques to m-dimensional complex Brownian motion.

Abstract

In this paper, we show an approximation in law of the complex Brownian motion by processes constructed from a stochastic process with independent increments. We give sufficient conditions for the characteristic function of the process with independent increments that ensure the existence of the approximation. We apply these results to L\'evy processes. Finally we extend this results to the $m$-dimensional complex Brownian motion.