@article{EJP55,
author = {Masatoshi Fukushima},
title = {On Semi-Martingale Characterizations of Functionals of Symmetric Markov Processes},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {4},
year = {1999},
keywords = {quasi-regular Dirichlet form, strongly regular representation, additive functionals, semimartingale, smooth signed measure, BV function},
abstract = {For a quasi-regular (symmetric) Dirichlet space $( {\cal E}, {\cal F})$ and an associated symmetric standard process $(X_t, P_x)$, we show that, for $u in {\cal F}$, the additive functional $u^*(X_t) - u^*(X_0)$ is a semimartingale if and only if there exists an ${\cal E}$-nest $\{F_n\}$ and positive constants $C_n$ such that $ \vert {\cal E}(u,v)\vert \leq C_n \Vert v\Vert_\infty, v \in {\cal F}_{F_n,b}.$ In particular, a signed measure resulting from the inequality will be automatically smooth. One of the variants of this assertion is applied to the distorted Brownian motion on a closed subset of $R^d$, giving stochastic characterizations of BV functions and Caccioppoli sets.},
pages = {no. 18, 1-32},
issn = {1083-6489},
doi = {10.1214/EJP.v4-55},
url = {http://ejp.ejpecp.org/article/view/55}}