Abstract
This chapter studies sample path properties of two exponential functionals of Brownian motion based on the integral tests for Brownian motion. Then one uses the relationship between one of them and the winding clock process of planar Brownian motion to give integral tests for the latter. The chapter also gives integral tests for the windings process of planar Brownian motion, Levy's stochastic area and the Cauchy process. In all cases, it significantly enlarges the classes of weight functions for which the integral tests hold. Brownian motion is point recurrent in dimension one, neighborhood recurrent, but not point recurrent in dimension two, and transient in dimension three and higher.
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