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.
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Eisenbaum, N. Integration with respect to local time. Potential Analysis 13, 303–328 (2000). https://doi.org/10.1023/A:1026440719120
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DOI: https://doi.org/10.1023/A:1026440719120