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

Jean Bertoin (1) , Marc Yor (2, 3)

1 Institut für Mathematik [Zürich]
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 IUF - Institut universitaire de France

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.

Mots clés: Occupation measure; finite variation; local times; change of variables formula

Domaines: Probabilités [math.PR]

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