On Fourier transform of generalized Brownian functionals

Hui-Hsiung Kuo

Journal of Multivariate Analysis, 1982, vol. 12, issue 3, 415-431

Abstract: Let 4 and 4 be the spaces of generalized Brownian functionals of the white noises B and b, respectively. A Fourier transform from 4 into 4 is defined by [phi](b) = [integral operator]0*: exp[-i [integral operator]1b(t) B(t) dt]: 1), where : : denotes the renormalization with respect to b and [mu] is the standard Gaussian measure on the space 0* of tempered distributions. It is proved that the Fourier transform carries B(t)-differentiation into multiplication by ib(t). The integral representation and the action of[phi] as a generalized Brownian functional are obtained. Some examples of Fourier transform are given.

Keywords: B(t)-differentiation; B(t)-multiplication; generalized; multiple; Wiener; integral; integral; representation; theorem; renormalization; test; functional; white; noise; Wiener-Ito; decomposition; theorem (search for similar items in EconPapers)
Date: 1982
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(82)90075-6
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:jmvana:v:12:y:1982:i:3:p:415-431

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

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().