B P International

Study on A Direct Construction of the Standard Brownian Motion

Gane Samb Lo1,2,3∗ , Aladji Babacar Niang1 and Harouna Sangare1,4

1LERSTAD, Gaston Berger University, Saint-Louis, Senegal.
2LSTA, Pierre and Marie Curie University, Paris VI, France.
3AUST – African University of Science and Technology, Abuja, Nigeria.
4DER MI, FST, Universite des Sciences, des Techniques et des Technologies de Bamako (USTT-B),


In this note, we combine the two approaches of Billingsley (1998) and Csorgo and Revesz (1980), to provide a detailed sequential and descriptive for creating a standard Brownian motion, from a Brownian motion whose time space is the class of non-negative dyadic numbers following the interpolation methof of Levy. By adding the proof of Etemadi’s inequality to text, it becomes self-readable and serves as an independent source for researchers and professors.

Keywords: Standard Brownian motion; Kolmogorov existence theorem; dyadic numbers; sequential construction.

ISBN: 978-93-90149-72-8 (Print) | 978-93-90149-22-3 (eBook)

Chapter DOI: https://doi.org/10.9734/bpi/tpmcs/v1/5056D

Volume DOI: https://doi.org/10.9734/bpi/tpmcs/v1

Published: August 17, 2020

Complete book available here: http://bp.bookpi.org/index.php/bpi/catalog/book/237