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Integral with respect to the $G$-Brownian local time (1212.6353v1)

Published 27 Dec 2012 in math.PR and math.FA

Abstract: Let ${\mathscr L}$ be the local time of $G$-Brownian motion $B$. In this paper, we prove the existence of the quadratic covariation $<f(B),B>{t}$ and the integral $\int{\mathbb R}f(x){\mathscr L}(dx,t)$. Moreover, a sublinear version of the Bouleau-Yor identity $$ \int_{\mathbb R}f(x){\mathscr L}(dx,t)=-<f(B),B>_{t} $$ is showed to hold under some suitable conditions. These allow us to write the It^o's formula for $C1$-functions.

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