Invariant, Super and Quasi-martingale Functions of a Markov Process

  • Lucian Beznea
  • Iulian CîmpeanEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)


We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with the process. Applications to semi-Dirichlet forms are given. We provide a unifying result which clarifies the relations between harmonic, co-harmonic, invariant, co-invariant, martingale and co-martingale functions, showing that in the conservative case they are all the same. Finally, using the co-excessive functions, we present a two-step approach to the existence of invariant probability measures.


Semimartingale Quasimartingale Markov process Invariant function Invariant measure 

Mathematics Subject Classification (2010)

60J45 31C05 60J40 60J25 37C40 37L40 31C25 



The first named author acknowledges support from the Romanian National Authority for Scientific Research, project number PN-III-P4-ID-PCE-2016-0372. The second named author acknowledges support from the Romanian National Authority for Scientific Research, project number PN-II-RU-TE-2014-4-0657.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Simion Stoilow Institute of Mathematics of the Romanian AcademyBucharestRomania
  2. 2.University of Bucharest, Faculty of Mathematics and Computer Science, and Centre Francophone en Mathématique de BucarestBucharestRomania

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