"Path properties of Cauchy's principal values related to local time"

Endre Csáki, Miklós Csörgö, Antónia Földes and Zhan Shi

Summary: Sample path properties of the Cauchy principal values of Brownian and random walk local times are studied. We establish LIL type results (without exact constants). Large and small increments are discussed. A strong approximation result between the above two processes is also proved.

Keywords: Additive functionals; principal values of Brownian and random walk local times; law of the iterated logarithm; large increments; modulus of continuity.

AMS 1991 subject classification: 60J15; 60F15; 60J55.