On Lévy’s Brownian motion and white noise space on the circle

Chunfeng Huang and Ao Li

Statistics & Probability Letters, 2021, vol. 171, issue C

Abstract: In this article, we show that the Brownian motion on the circle constructed by Lévy (1959) is a regular Euclidean Brownian motion on the half-circle with its own mirror image on the other half-circle, and is degenerated in the sense of Minlos (1959). This raises the question of what the white noise is on the circle. We then formally define the white noise space and its associated Brownian bridge on the circle.

Keywords: Brownian bridge; Gel’fand Triple; Generalized random process (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715221000031
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:171:y:2021:i:c:s0167715221000031

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2021.109041

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().