Where do Brownian particles spend their time?

We study statistical properties of the fraction of time spent by a Brownian particle in different regions of space. Also treated in our analysis are the effects of one or more constraints on the trajectory at different times. We show that the effects of imposing n constraints can be analyzed in terms of the probability density of the residence time for a single constraint. An analogy to the description of the spatial density of a polymer chain is proposed and applied to evaluate the monomeric density in some specific examples.