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

Endre Csáki, Miklós Csörgö, Antónia Földes and Zhan Shi

Summary: 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. Lévy; (b) the large increments of $Y$.

Keywords: Local time; modulus of continuity; large increment; Brownian motion.

AMS 1991 subject classification: 60J65.