Maximums on trees

Predrag R. Jelenković and Mariana Olvera-Cravioto

Stochastic Processes and their Applications, 2015, vol. 125, issue 1, 217-232

Abstract: We study the minimal/endogenous solution R to the maximum recursion on weighted branching trees given by R=D(⋁i=1NCiRi)∨Q, where (Q,N,C1,C2,…) is a random vector with N∈N∪{∞}, P(|Q|>0)>0 and nonnegative weights {Ci}, and {Ri}i∈N is a sequence of i.i.d. copies of R independent of (Q,N,C1,C2,…); =D denotes equality in distribution. Furthermore, when Q>0 this recursion can be transformed into its additive equivalent, which corresponds to the maximum of a branching random walk and is also known as a high-order Lindley equation. We show that, under natural conditions, the asymptotic behavior of R is power-law, i.e., P(|R|>x)∼Hx−α, for some α>0 and H>0. This has direct implications for the tail behavior of other well known branching recursions.

Keywords: High-order Lindley equation; Stochastic fixed-point equations; Weighted branching processes; Branching random walk; Power law distributions; Large deviations; Cramér–Lundberg approximation; Random difference equations; Maximum recursion (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414914002099
Full text for ScienceDirect subscribers only

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:eee:spapps:v:125:y:2015:i:1:p:217-232

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2014.09.004

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().