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

Xavier Bardina; Giulia Binotto; Carles Rovira

doi:10.1016/j.jmaa.2016.06.061

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

Xavier Bardina, Giulia Binotto, Carles Rovira

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 Citations (Scopus)

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 language	English
Pages (from-to)	700-720
Journal	Journal of Mathematical Analysis and Applications
Volume	444
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2016.06.061
Publication status	Published - 1 Dec 2016

Keywords

Complex Brownian motion
Strong convergence
Weak convergence

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title = "The complex Brownian motion as a strong limit of processes constructed from a Poisson process",

abstract = "{\textcopyright} 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.",

keywords = "Complex Brownian motion, Strong convergence, Weak convergence",

author = "Xavier Bardina and Giulia Binotto and Carles Rovira",

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T1 - The complex Brownian motion as a strong limit of processes constructed from a Poisson process

AU - Bardina, Xavier

AU - Binotto, Giulia

AU - Rovira, Carles

PY - 2016/12/1

Y1 - 2016/12/1

N2 - © 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.

AB - © 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.

KW - Complex Brownian motion

KW - Strong convergence

KW - Weak convergence

U2 - 10.1016/j.jmaa.2016.06.061

DO - 10.1016/j.jmaa.2016.06.061

M3 - Article

VL - 444

SP - 700

EP - 720

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -