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Local time as an element of the Sobolev space

Local time as an element of the Sobolev space

For a centered Gaussian random ?eld taking its values in R^d, we investigate the existence of a local time as a generalized functional, i.e an element of some Sobolev space. We give the sfficient condition for such an existence in terms of the field covariation and apply it in several examples: the...

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Bibliographic Details
Main Author: Rudenko, A.V.
Format: Article
Language:English
Published: Інститут математики НАН України 2007
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/4508
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Summary:For a centered Gaussian random ?eld taking its values in R^d, we investigate the existence of a local time as a generalized functional, i.e an element of some Sobolev space. We give the sfficient condition for such an existence in terms of the field covariation and apply it in several examples: the self-intersection local time for a fractional Brownian motion and the intersection local time for two Brownian motions.

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