报告人：Guy Latouche 教授
报告题目：Markov modulated Brownian motion with a sticky boundary
We analyze the stationary distribution of regulated Markov modulated Brownian motions (MMBM) modified so that their evolution is slowed down when the process reaches level zero --- level zero is said to be sticky.
To determine the stationary distribution, we extend to MMBMs a construction of Brownian motion with sticky boundary, and we follow a Markov-regenerative approach similar to the one developed in past years in the context of quasi-birth-and-death processes and fluid queues. We also rely on recent work showing that Markov-modulated Brownian motions may be analyzed as limits of a parametrized family of fluid queues.