Translator Disclaimer
June 2014 Tail asymptotics of the stationary distribution of a two-dimensional reflecting random walk with unbounded upward jumps
Masahiro Kobayashi, Masakiyo Miyazawa
Author Affiliations +
Adv. in Appl. Probab. 46(2): 365-399 (June 2014). DOI: 10.1239/aap/1401369699

Abstract

We consider a two-dimensional reflecting random walk on the nonnegative integer quadrant. This random walk is assumed to be skip free in the direction to the boundary of the quadrant, but may have unbounded jumps in the opposite direction, which are referred to as upward jumps. We are interested in the tail asymptotic behavior of its stationary distribution, provided it exists. Assuming that the upward jump size distributions have light tails, we find the rough tail asymptotics of the marginal stationary distributions in all directions. This generalizes the corresponding results for the skip-free reflecting random walk in Miyazawa (2009). We exemplify these results for a two-node queueing network with exogenous batch arrivals.

Citation

Download Citation

Masahiro Kobayashi. Masakiyo Miyazawa. "Tail asymptotics of the stationary distribution of a two-dimensional reflecting random walk with unbounded upward jumps." Adv. in Appl. Probab. 46 (2) 365 - 399, June 2014. https://doi.org/10.1239/aap/1401369699

Information

Published: June 2014
First available in Project Euclid: 29 May 2014

zbMATH: 1316.60066
MathSciNet: MR3215538
Digital Object Identifier: 10.1239/aap/1401369699

Subjects:
Primary: 60K25, 60K25
Secondary: 60F10, 60G50

Rights: Copyright © 2014 Applied Probability Trust

JOURNAL ARTICLE
35 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.46 • No. 2 • June 2014
Back to Top