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Integration with respect to local time

Authors:	Eisenbaum Nathalie

Institution:	(1) Indian Statistical Institute, Bangalore Centre, 8th Mile Mysore Road, R.V. College P.O, 560059 Bangalore, India

Abstract:	Let $\left( {L_t^x ;x \in \mathbb{R},t \geqslant 0} \right)$ be the local time process of a linear Brownian motion B. We integrate the Borel functions on $\mathbb{R}_ \times \mathbb{R}_ +$ with respect to $\left( {L_t^x ;x \in \mathbb{R},t \geqslant 0} \right)$ . This allows us to write Itôrs formula for new classes of functions, and to define a local time process of B on any borelian curve. Some results are extended from deterministic to random functions.

Keywords:	Brownian motion local time stochastic integration Itô formula
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