Thin tails of fixed points of the nonhomogeneous smoothing transform

Gerold Alsmeyer and Piotr Dyszewski

Stochastic Processes and their Applications, 2017, vol. 127, issue 9, 3014-3041

Abstract: For a given random sequence (C,T1,T2,…), the smoothing transform S maps the law of a real random variable X to the law of ∑k≥1TkXk+C, where X1,X2,… are independent copies of X and also independent of (C,T1,T2,…). This law is a fixed point of S if X=d∑k≥1TkXk+C holds true, where =d denotes equality in law. Under suitable conditions including EC=0, S possesses a unique fixed point within the class of centered distributions, called the canonical solution because it can be obtained as a certain martingale limit in an associated weighted branching model. The present work provides conditions on (C,T1,T2,…) such that the canonical solution exhibits right and/or left Poissonian tails and the abscissa of convergence of its moment generating function can be determined. As a particular application, the right tail behavior of the Quicksort distribution is found.

Keywords: Nonhomogeneous smoothing transform; Stochastic fixed point; Moment generating function; Exponential moment; Poissonian tail; Weighted branching process; Forward and backward equation; Quicksort distribution (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414917300236
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:127:y:2017:i:9:p:3014-3041

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.2017.01.008

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 ().