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Müntz linear transforms of Brownian motion
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Alili, Larbi and Wu, Ching-Tang (2014) Müntz linear transforms of Brownian motion. Electronic Journal of Probability, Volume 19 . Article number 36. doi:10.1214/EJP.v19-2424 ISSN 1083-6489.
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Official URL: http://dx.doi.org/10.1214/EJP.v19-2424
Abstract
We consider a class of Volterra linear transforms of Brownian motion associated to a sequence of Müntz Gaussian spaces and determine explicitly their kernels; the kernels take a simple form when expressed in terms of Müntz-Legendre polynomials. These are new explicit examples of progressive Gaussian enlargement of a Brownian filtration. We give a necessary and sufficient condition for the existence of kernels of infinite order associated to an infinite dimensional Müntz Gaussian space; we also examine when the transformed Brownian motion remains a semimartingale in the filtration of the original process. This completes some already obtained partial answers to the aforementioned problems in the infinite dimensional case.
| 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, Transformations (Mathematics) | ||||
| Journal or Publication Title: | Electronic Journal of Probability | ||||
| Publisher: | University of Washington. Dept. of Mathematics | ||||
| ISSN: | 1083-6489 | ||||
| Official Date: | 22 March 2014 | ||||
| Dates: |
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| Volume: | Volume 19 | ||||
| Article Number: | Article number 36 | ||||
| DOI: | 10.1214/EJP.v19-2424 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||
| Date of first compliant deposit: | 28 December 2015 | ||||
| Date of first compliant Open Access: | 28 December 2015 | ||||
| Funder: | France. Agence nationale de la recherche (ANR) | ||||
| Grant number: | ANR-09-Blan-0084-01 (ANR) | ||||
| Open Access Version: |
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