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

Xavier Bardina and Carles Rovira

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona 08193 Bellaterra, Barcelona
Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007-Barcelona

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 sucient conditions for the characteristic
function of the process with independent increments that ensure the existence of the approximation. We apply these results to Lévy processes. Finally we extend this results to the m-dimensional complex Brownian
motion.

Keywords: weak convergence, complex Brownian motion, Lévy processes

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