par Latouche, Guy 
;Nguyen, Giang
Référence Stochastic models, 33, 2, page (297-321)
Publication Publié, 2017-04
;Nguyen, Giang Référence Stochastic models, 33, 2, page (297-321)
Publication Publié, 2017-04
Article révisé par les pairs
| Résumé : | 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. |
