Penalization of Galton–Watson Trees with Marked Vertices

Abraham Romain (), Boulal Sonia () and Debs Pierre ()
Additional contact information
Abraham Romain: Université d’Orléans, Université de Tours, CNRS
Boulal Sonia: Université d’Orléans, Université de Tours, CNRS
Debs Pierre: Université d’Orléans, Université de Tours, CNRS

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3688-3724

Abstract: Abstract We consider a Galton–Watson tree where each node is marked independently of each other with a probability depending on its out-degree. Using a penalization method, we exhibit new martingales where the number of marks up to level $$n-1$$ n - 1 appears. Then, we use these martingales to define new probability measures via a Girsanov transformation and describe the distribution of the random trees under these new probabilities.

Keywords: Marked Galton–Watson tree; Martingales; Girsanov transformation; Penalization; 60J80; 60G42 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-024-01364-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:37:y:2024:i:4:d:10.1007_s10959-024-01364-y

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-024-01364-y

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().