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

Published 23 Sep 2015 in math.PR | (1509.07116v1)

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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