Quadratic variation of potentials and harmonic functions

Abstract

We prove the existence of a finite quadratic variation for stochastic processes u ( Y ) u(Y) , where Y is Brownian motion on a Green domain of R n {R^n} , stopped upon reaching the Martin boundary, and u is a positive superharmonic function on the domain. As by-products we have results which are also of interest from a non-probabilistic point of view.