XII: 57, 763-769, LNM 649 (1978)
MEYER, Paul-André
La formule d'Ito pour le mouvement brownien, d'après Brosamler (Brownian motion, Stochastic calculus)
This paper presents the results of a paper by Brosamler (Trans. Amer. Math. Soc. 149, 1970) on the Ito formula $f(B_t)=...$ for $n$-dimensional Brownian motion, under the weakest possible assumptions: namely up to the first exit time from an open set $W$ and assuming only that $f$ is locally in $L^1$ in $W$, and its Laplacian in the sense of distributions is a measure in $W$
Keywords: Ito formula
Nature: Exposition
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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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