Reflecting Brownian motion in three dimensions: a new proof of sufficient conditions for positive recurrence

J. Dai () and J. Harrison

Mathematical Methods of Operations Research, 2012, vol. 75, issue 2, 135-147

Abstract: Let Z = {Z(t), t ≥ 0} be a semimartingale reflecting Brownian motion that lives in the three-dimensional non-negative orthant. A 2002 paper by El Kharroubi, Ben Tahar and Yaacoubi gave sufficient conditions for positive recurrence of Z. Recently Bramson, Dai and Harrison have shown that those conditions are also necessary for positive recurrence. In this paper we provide an alternative proof of sufficiency, the salient feature of which is its use of a linear Lyapunov function. Copyright Springer-Verlag 2012

Keywords: Reflecting Brownian motion; Skorohod problem; Fluid model; Positive recurrence; Queueing networks; Heavy traffic; Diffusion approximation (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-010-0304-7 (text/html)
Access to full text is restricted to subscribers.

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:mathme:v:75:y:2012:i:2:p:135-147

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-010-0304-7

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().