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arXiv · 0803.3522

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

Xavier Bardina·Carles Rovira
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Abstract

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 Itô's s formula as an integral over space and time with respect to local time.

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Xavier Bardina, Carles Rovira. 2008-03-25. Integration with respect to local time and Ito's formula for smooth nondegenerate martingales. https://arxiv.org/abs/0803.3522

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