Abstract
In this chapter, the existence and regularity properties of local times associated to a continuous semimartingale are shown. Some martingales involving the local times are constructed. Existence of principal values for Brownian motion is deduced from the regularity of Brownian local times. Itô’s formula for Brownian motion is extended to integrals of square integrable functions. A balayage formula is shown. Local times are seen to arise in the computations of compensators of last passage times.
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Yen, JY., Yor, M. (2013). The Existence and Regularity of Semimartingale Local Times. In: Local Times and Excursion Theory for Brownian Motion. Lecture Notes in Mathematics, vol 2088. Springer, Cham. https://doi.org/10.1007/978-3-319-01270-4_2
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DOI: https://doi.org/10.1007/978-3-319-01270-4_2
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