We develop some topics about Brownian motion with a particular emphasis on the study of principal values of Brownian local times. We show some links between principal values and Doob’s $h$-transforms of Brownian motion, for nonpositive harmonic functions $h$. We also give a survey and complement some martingale approaches to Ray–Knight theorems for local times.
"Some Brownian functionals and their laws." Ann. Probab. 25 (3) 1011 - 1058, July 1997. https://doi.org/10.1214/aop/1024404505