Journal of Jilin University Science Edition ›› 2023, Vol. 61 ›› Issue (3): 509-516.

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Dirichlet Forms in Continuous-Time Guichardet-Fock Space

LI Xiaohui1, ZHOU Yulan2, FANG Yanbing1, ZHANG Yin3   

  1. 1. School of Advanced Interdisciplinary Studies, Ningxia University, Zhongwei 755099,  Ningxia Hui Autonomous Region, China;
    2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070,  China;
    3. School of Intelligence Technology, Geely University of China, Chengdu 641402, China
  • Received:2022-08-24 Online:2023-05-26 Published:2023-05-26

Abstract: Firstly, we study the Dirichlet forms (ε,Dom ε) in continuous-time Guichardet-Fock space L2(Γ;η) by means of multiple integral of bounded operator, and obtain the relation. Secondly, we consider a class of operator semigroups and prove the relation.

Key words: Dirichlet form, weighted number operator, point-state modified stochastic gradient

CLC Number: 

  • O211