Abstract
We prove the equivalence of the local property for an irreducible regular Dirichlet form and the Markov property for the Gaussian field associated with the Dirichlet form. Moreover we introduce a strong Markov property for Gaussian fields and present some sufficient conditions for this to hold.
Acknowledgments
I would like to thank Professor Takashi Kumagai for helpful discussions and comments. I appreciate Professor David A. Croydon and Professor Naotaka Kajino for checking the introduction of this paper. I thank Professor Masatoshi Fukushima for useful comments on how the Markov property is used (Remark 2.4). I also thank the referee for useful comments and for pointing out typos. This work was supported by JSPS KAKENHI Grant Number JP21J20251.
Citation
Takumu Ooi. "Markov properties for Gaussian fields associated with Dirichlet forms." Osaka J. Math. 60 (3) 579 - 595, July 2023.
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