Quadratic Variation of Potentials and Harmonic Functions

Abstract

We prove the existence of a finite quadratic variation for stochastic processes $u(Y)$, where Y is Brownian motion on a Green domain of ${R^n}$, 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.

Locations

• Transactions of the American Mathematical Society - View - PDF