Approximations of a Complex Brownian Motion by Processes Constructed from a L,vy Process

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 to the characteristic function of the process with independent increments that ensure the existence of such an approximation. We apply these results to L,vy processes. Finally we extend these results to the m-dimensional complex Brownian motion.