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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Quadratic variation of potentials and harmonic functions


Author: Gunnar A. Brosamler
Journal: Trans. Amer. Math. Soc. 149 (1970), 243-257
MSC: Primary 60.62
MathSciNet review: 0270442
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0270442-1
PII: S 0002-9947(1970)0270442-1
Keywords: Quadratic variation of martingales, classical probabilistic potential theory, additive functionals of Brownian motion, Ito formula
Article copyright: © Copyright 1970 American Mathematical Society