Slowing time: Markov-modulated Brownian motions with a sticky boundary. Issue 2 (3rd April 2017)

• Record Type: Journal Article
• Authors: Latouche, Guy; Nguyen, Giang T.
• Is Part Of: Stochastic models. Volume 33:Issue 2(2017)
• Page Start: 297
• Page End: 321
• Publication Date: 2017-04-03
• Subjects: Fluid queues -- Markov-modulated Brownian motion -- regenerative processes -- sticky boundary; 60J65 -- 60J55 -- 60F17; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2017.1284000
• Languages: English
• ISSNs: 1532-6349

Abstract

ABSTRACT: We define a new family of stochastic processes called Markov modulated Brownian motions with a sticky boundary at zero. Intuitively, each process is a regulated Markov-modulated Brownian motion whose boundary behavior is modified to slow down at level zero. To determine the stationary distribution of a sticky MMBM, we follow a Markov-regenerative approach similar to the one developed with great success in the context of quasi-birth-and-death processes and fluid queues. Our analysis also relies on recent work showing that Markov-modulated Brownian motions arise as limits of a parametrized family of fluid queues.