Local times for functions with finite variation: two versions of Stieltjes change of variables formula

2013/07/04 by Bertoin, Jean, Yor, Marc
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1307.1288

Abstract

We introduce two natural notions for the occupation measure of a function V with finite variation. The first yields a signed measure, and the second a positive measure. By comparing two versions of the change-of-variables formula, we show that both measures are absolutely continuous with respect to Lebesgue measure. Occupation densities can be thought of as local times of V, and are described by a Meyer-Tanaka like formula.

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