Local time as an element of the Sobolev space

• Date: 2007
• ISSN: 0321-3900
• Main Author: Rudenko, A.V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/4508
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Local time as an element of the Sobolev space / A.V. Rudenko // Theory of Stochastic Processes. — 2007. — Т. 13 (29), № 3. — С. 65–79. — Бібліогр.:12 назв.— англ.

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...