XVI: 21, 238-247, LNM 920 (1982)
YOR, Marc
Sur la transformée de Hilbert des temps locaux browniens et une extension de la formule d'Itô (Brownian motion)
This paper is about the application to the function $(x-a)\log|x-a|-(x-a)$ (whose second derivative is $1/x-a$) of the Ito-Tanaka formula; the last term then involves a formal Hilbert transform $\tilde L^a_t$ of the local time process $L^a_t$. Such processes had been defined by Ito and McKean, and studied by Yamada as examples of Fukushima's ``additive functionals of zero energy''. Here it is proved, as a consequence of a general theorem, that this process has a jointly continuous version---more precisely, Hölder continuous of all orders $<1/2$ in $a$ and in $t$
Comment: For a modern version with references see Yor, Some Aspects of Brownian Motion II, Birkhäuser 1997
Keywords: Local times, Hilbert transform, Ito formula
Nature: Original
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