Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Quasimartingales associated to Markov processes


Authors: Lucian Beznea and Iulian Cîmpean
Journal: Trans. Amer. Math. Soc. 370 (2018), 7761-7787
MSC (2010): Primary 60J45, 31C25, 60J40; Secondary 60J25, 60J35, 60J55, 60J57, 31C05
DOI: https://doi.org/10.1090/tran/7214
Published electronically: May 3, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a fixed right process $ X$ we investigate those functions $ u$ for which $ u(X)$ is a quasimartingale. We prove that $ u(X)$ is a quasimartingale if and only if $ u$ is the difference of two finite excessive functions. In particular, we show that the quasimartingale nature of $ u$ is preserved under killing, time change, or Bochner subordination. The study relies on an analytic reformulation of the quasimartingale property for $ u(X)$ in terms of a certain variation of $ u$ with respect to the transition function of the process. We provide sufficient conditions under which $ u(X)$ is a quasimartingale, and finally, we extend to the case of semi-Dirichlet forms a semimartingale characterization of such functionals for symmetric Markov processes, due to Fukushima.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 60J45, 31C25, 60J40, 60J25, 60J35, 60J55, 60J57, 31C05

Retrieve articles in all journals with MSC (2010): 60J45, 31C25, 60J40, 60J25, 60J35, 60J55, 60J57, 31C05


Additional Information

Lucian Beznea
Affiliation: Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit No. 2, P.O. Box 1-764, RO-014700 Bucharest, Romania—and—University of Bucharest, Faculty of Mathematics and Computer Science, and Centre Francophone en Mathématique de Bucarest, Romania.
Email: lucian.beznea@imar.ro

Iulian Cîmpean
Affiliation: Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit No. 2, P.O. Box 1-764, RO-014700 Bucharest, Romania
Email: iulian.cimpean@imar.ro

DOI: https://doi.org/10.1090/tran/7214
Keywords: Semimartingale, quasimartingale, Markov process, excessive function, Dirichlet form, Fukushima decomposition, smooth measure.
Received by editor(s): October 24, 2016
Received by editor(s) in revised form: February 8, 2017
Published electronically: May 3, 2018
Additional Notes: The first author acknowledges support from the Romanian National Authority for Scientific Research, project number PN-III-P4-ID-PCE-2016-0372.
The second author acknowledges support from the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-0007.
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society