- Markov-modulated Brownian motion with two reflecting barriers
- Journal of Applied Probability
- Volume | Issue number
- 47 | 4
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
We consider a Markov-modulated Brownian motion reflected to stay in a strip [0, B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this result and explain its simplicity. Moreover, this argument allows for generalizations including the distribution of the reflected process at an independent, exponentially distributed epoch. Our second contribution concerns transient behavior of the model. We identify the joint law of the processes defining the model at inverse local times.
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