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On Semi-Martingale Characterizations of Functionals of Symmetric Markov Processes


 
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1. Title Title of document On Semi-Martingale Characterizations of Functionals of Symmetric Markov Processes
 
2. Creator Author's name, affiliation, country Masatoshi Fukushima; Kansai University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) quasi-regular Dirichlet form, strongly regular representation, additive functionals, semimartingale, smooth signed measure, BV function
 
3. Subject Subject classification 60J 45, 60J 55, 31C 25
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1999-10-06
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/55
 
10. Identifier Digital Object Identifier 10.1214/EJP.v4-55
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 4
 
12. Language English=en
 
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