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Müntz linear transforms of Brownian motion

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1.	Title	Title of document	Müntz linear transforms of Brownian motion
2.	Creator	Author's name, affiliation, country	Larbi Alili; University of Warwick; United Kingdom
2.	Creator	Author's name, affiliation, country	Ching-Tang Wu; National Taitung University; Taiwan, Province of China
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Enlargement of filtration ; Gaussian process ; M\"untz polynomials ; noncanonical representation ; self-reproducing kernel ; Volterra representation
3.	Subject	Subject classification	45D05 ; 60G15
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	ANR-09-Blan-0084-01
7.	Date	(YYYY-MM-DD)	2014-03-22
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2424
10.	Identifier	Digital Object Identifier	10.1214/EJP.v19-2424
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 19
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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