The Library
Coupling of Brownian motions in Banach spaces
Tools
Candellero, Elisabetta and Kendall, W. S. (2018) Coupling of Brownian motions in Banach spaces. Electronic Communication in Probability, 23 . 9. doi:10.1214/18-ECP109 ISSN 1083-589X.
|
PDF
WRAP-coupling-Brownian-motions-Banach-spaces-Kendall-2018.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (847Kb) | Preview |
|
PDF
WRAP-coupling-Brownian-motions-Banach-spaces-Kendall-2018.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (311Kb) |
Official URL: https://doi.org/10.1214/18-ECP109
Abstract
Consider a separable Banach space W supporting a non-trivial Gaussian measure μ. The following is an immediate consequence of the theory of Gaussian measure on Banach spaces: there exist (almost surely) successful couplings of two W-valued Brownian motions B and B˜ begun at starting points B(0) and B˜(0) if and only if the difference B(0)−B˜(0) of their initial positions belongs to the Cameron-Martin space Hμ of W corresponding to μ. For more general starting points, can there be a “coupling at time ∞”, such that almost surely ∥B(t)−B˜(t)∥W→0 as t→∞? Such couplings exist if there exists a Schauder basis of W which is also a Hμ-orthonormal basis of Hμ. We propose (and discuss some partial answers to) the question, to what extent can one express the probabilistic Banach space property “Brownian coupling at time ∞ is always possible” purely in terms of Banach space geometry?
Item Type: | Journal Article | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | |||||||||
Library of Congress Subject Headings (LCSH): | Brownian motion processes, Banach spaces, Gaussian measures, Hilbert space | |||||||||
Journal or Publication Title: | Electronic Communication in Probability | |||||||||
Publisher: | Institute of Mathematical Statistics | |||||||||
ISSN: | 1083-589X | |||||||||
Official Date: | 16 January 2018 | |||||||||
Dates: |
|
|||||||||
Volume: | 23 | |||||||||
Article Number: | 9 | |||||||||
DOI: | 10.1214/18-ECP109 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||
Date of first compliant deposit: | 26 January 2018 | |||||||||
Date of first compliant Open Access: | 28 February 2018 | |||||||||
RIOXX Funder/Project Grant: |
|
|||||||||
Related URLs: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year