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Measure-valued discrete branching Markov processes


Authors: Lucian Beznea and Oana Lupaşcu
Journal: Trans. Amer. Math. Soc. 368 (2016), 5153-5176
MSC (2010): Primary 60J80, 60J45, 60J35; Secondary 60J40, 47D07
DOI: https://doi.org/10.1090/tran/6514
Published electronically: October 29, 2015
MathSciNet review: 3456175
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Abstract: We construct and study branching Markov processes on the space of finite configurations of the state space of a given standard process, controlled by a branching kernel and a killing kernel. In particular, we may start with a superprocess, obtaining a branching process with state space the finite configurations of positive finite measures on a topological space. A main tool in proving the path regularity of the branching process is the existence of convenient superharmonic functions having compact level sets, allowing the use of appropriate potential theoretical methods.


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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 – Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania
Email: lucian.beznea@imar.ro

Oana Lupaşcu
Affiliation: Simion Stoilow Institute of Mathematics of the Romanian Academy, Research group of the POSDRU Project 82514, Bucharest, Romania
Address at time of publication: Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest, Romania – and – Research Institute of the University of Bucharest (ICUB), Bucharest, Romania
Email: oana.lupascu@imar.ro

DOI: https://doi.org/10.1090/tran/6514
Keywords: Discrete branching process, measure-valued process, branching kernel, branching semigroup, excessive function, standard process, compact Lyapunov function
Received by editor(s): January 1, 2013
Received by editor(s) in revised form: July 14, 2014
Published electronically: October 29, 2015
Additional Notes: This work was supported by a grant from the Romanian National Authority for Scientific Research, CNCS –UEFISCDI, project number PN-II-ID-PCE-2011-3-0045.
The second author’s research was financed through the project “Excellence Research Fellowships for Young Researchers”, the 2015 Competition, founded by the Research Institute of the University of Bucharest (ICUB)
Article copyright: © Copyright 2015 American Mathematical Society