Beta-type operators preserve shape properties

JoséA. Adell, F. Germán Badía and Jesús de la Cal

Stochastic Processes and their Applications, 1993, vol. 48, issue 1, 1-8

Abstract: In this paper, we show that several integral operators, which are associated with beta-type probability distributions, preserve monotonicity and convexity, as well as the property of being absolutely or completely monotone. Simple proofs are given by using probabilistic methods, in particular, representations of these operators in terms of appropriate stochastic processes with stationary independent increments (referred to as 'gamma' processes). As a consequence, similar properties for other Bernstein-type operators closely related to them are obtained.

Keywords: Beta-type; operators; gamma; processes; monotone; and; convex; funtions (search for similar items in EconPapers)
Date: 1993
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(93)90104-C
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:48:y:1993:i:1:p:1-8

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

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 ().