The complex Brownian motion as a strong limit of processes constructed from a Poisson process

2015/09/23 by Xavier Bardina, Bardina, Xavier, Giulia Binotto +3
Economics, Econometrics and Finance · #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1509.07116

Abstract

We construct a family of processes, from a single Poisson process, that converges in law to a complex Brownian motion. Moreover, we find realizations of these processes that converge almost surely to the complex Brownian motion, uniformly on the unit time interval. Finally the rate of convergence is derived.

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