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

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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https://hal.archives-ouvertes.fr/hal-00835685
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Submitted on : Thursday, July 4, 2013 - 12:42:37 PM
Last modification on : Tuesday, May 14, 2019 - 11:08:21 AM
Long-term archiving on: Saturday, October 5, 2013 - 4:17:31 AM

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  • HAL Id : hal-00835685, version 2
  • ARXIV : 1307.1288

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Jean Bertoin, Marc Yor. Local times for functions with finite variation: two versions of Stieltjes change of variables formula. 2013. ⟨hal-00835685v2⟩

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