Flux and Lateral Conditions for Symmetric Markov Processes |
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Authors: | Zhen-Qing Chen Masatoshi Fukushima |
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Institution: | (1) Department of Mathematics, University of Washington, Seattle, WA 98195, USA;(2) Branch of Mathematical Science, Osaka University, Toyonaka Osaka, 560-0043, Japan |
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Abstract: | The purpose of this paper is to give an affirmative answer at infinitesimal generator level to the 40 years old Feller’s boundary
problem for symmetric Markov processes with general quasi-closed boundaries. For this, we introduce a new notion of flux functional,
which can be intrinsically defined via the minimal process X
0 in the interior. We then use it to characterize the L
2-infinitesimal generator of a symmetric process that extends X
0. Special attention is paid to the case when the boundary consists of countable many points possessing no accumulation points.
Research of Masatoshi Fukushima was supported by Grand-in-Aid for Scientific Research of MEXT No.19540125. |
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Keywords: | Symmetric Markov process Infinitesimal generator Flux Lateral condition Boundary Martingale Reflected Dirichlet space Boundary theory Extension process Feller measures Jumping measure Killing measure Skew Brownian motion |
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