On Semi-martingale Characterizations of Functionals of Symmetric Markov Processes
نویسنده
چکیده
Abstract For a quasi-regular (symmetric) Dirichlet space (E ,F) and an associated symmetric standard process (Xt, Px), we show that, for u ∈ F , the additive functional u∗(Xt) − u∗(X0) is a semimartingale if and only if there exists an E-nest {Fn} and positive constants Cn such that |E(u, v)| ≤ Cn‖v‖∞, v ∈ FFn,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 Rd, giving stochastic characterizations of BV functions and Caccioppoli sets.
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