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Positivity Preserving Semigroups and Positivity Preserving Coercive Forms

  • Xian Chen
  • Zhi-Ming MaEmail author
  • Xue Peng
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)

Abstract

We recall the idea of Ma and Röckner (Canad. J. Math., 47:817–840, 1995, [13]) and report some further progress along the line of the research initiated by Ma and Röckner (Canad. J. Math., 47:817–840, 1995, [13]). The further progress includes the technique of \(h\hat{h}\)-transformations for positivity preserving semigroups, and includes our recent results on (\(\sigma \)-finite) distribution flows associated with a given positivity preserving coercive form, which is independent of the choice of h, and equipped with which the canonical cadlag process behaves like a strong Markov process.

Keywords

Positivity preserving coercive form h-associated process \(h{\hat{h}}\)-transform Distribution flow Revuz correspondence 

MSC 2010

Primary 31C25 47D03 Secondary 60J40 60J45 31C15 

Notes

Acknowledgements

We thank X.F. Han and W. Sun for permitting us to present our joint work here. Z.M. Ma is grateful to S. Albeverio and M. Röckner for the long standing pleasant collaboration. We are indebted to M. Fukushima who brought our attention to the work of pseudo Hunt processes introduced in [15], which stimulated the research of distribution flows. We are grateful to Y. Oshima who sent us his manuscript [15] which helps our research. We thank Mufa Chen, Zhenqing Chen and Michael Röckner for their comments and discussions. We are grateful to the support of National Center for Mathematics and Interdisciplinary Sciences (NCMIS), and NSFC project (11526214).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesXiamen UniversityXiamenChina
  2. 2.AMSS, University of Chinese Academy of SciencesBeijingChina
  3. 3.College of MathematicsSichuan UniversityChengduChina

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