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

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Abstract

© 2016 Elsevier Inc. 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.
Original languageEnglish
Pages (from-to)700-720
JournalJournal of Mathematical Analysis and Applications
Volume444
Issue number1
DOIs
Publication statusPublished - 1 Dec 2016

Keywords

  • Complex Brownian motion
  • Strong convergence
  • Weak convergence

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