Abstract
We consider a Brownian motion with time-reversible Markov-modulated speed and two reflecting barriers. A methodology depending on a certain multidimensional martingale together with some linear algebra is applied in order to explicitly compute the stationary distribution of the joint process of the content level and the state of the underlying Markov chain. It is shown that the stationary distribution is such that the two quantities are independent. The long-run average push at the two barriers at each of the states is also computed.
| Original language | English |
|---|---|
| Pages (from-to) | 1237-1242 |
| Number of pages | 6 |
| Journal | Journal of Applied Probability |
| Volume | 41 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 2004 |
Keywords
- Brownian motion
- Double barrier
- Markov modulated
- Multidimensional martingale
- Reflected Brownian motion
- State-dependent speed
- Two-sided reflection