Integration with respect to local time and Ito's formula for smooth nondegenerate martingales

Details Integration with respect to local time and Ito's formula for smooth nondegenerate martingales Integration with respect to local time and Ito's formula for smooth nondegenerate martingales

2008-03-25

arxiv.org/abs/0803.3522v1

Mathematics

Probability

Scientific paper

We show an It\^ o's formula for nondegenerate Brownian martingales
$X_t=\int_0^t u_s dW_s$ and functions $F(x,t)$ with locally integrable
derivatives in $t$ and $x$. We prove that one can express the additional term
in It\^o's s formula as an integral over space and time with respect to local
time.

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