### LOCAL TIME AS AN ELEMENT OF THE SOBOLEV SPACE

**ALEXEY V. RUDENKO**

*Theory of Stochastic Processes*

*Vol. 13 (29), no. 3, 2007, pp. 65–79*

For a centered Gaussian random field taking its values in $\mathbb{R}^d$, we investigate the existence of a local time as a generalized functional, i.e an element of some Sobolev space. We give the sufficient 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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