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Potential Analysis

, Volume 13, Issue 4, pp 303–328 | Cite as

Integration with respect to local time

  • Nathalie Eisenbaum
Article

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.

Brownian motion local time stochastic integration Itô formula 

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© Kluwer Academic Publishers 2000

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  • Nathalie Eisenbaum

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