# 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2013
Domaine :

https://hal.archives-ouvertes.fr/hal-00835685
Contributeur : Jean Bertoin <>
Soumis le : jeudi 4 juillet 2013 - 12:42:37
Dernière modification le : mardi 11 octobre 2016 - 14:04:59
Document(s) archivé(s) le : samedi 5 octobre 2013 - 04:17:31

### Fichiers

Local_times.pdf
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### Identifiants

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

### Citation

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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## 175

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