Quadratic variation of potentials and harmonic functions
Quadratic variation of potentials and harmonic functions
We prove the existence of a finite quadratic variation for stochastic processes <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u left-parenthesis upper Y right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>Y</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">u(Y)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <italic>Y</italic> is Brownian motion on a Green domain of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper …