Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Increment sizes of the principal value of Brownian local time

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Résumé: Let $W$ be a standard Brownian motion, and define $Y(t)= \int_0^t ds/W(s)$ as Cauchy's principal value related to local time. We determine: (a) the modulus of continuity of $Y$ in the sense of P. L\'evy; (b) the large increments of $Y$.