Title：Markov modulated Brownian motion with a sticky boundary
Venue：Room 145 ，Math Building
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.