Article ID: | iaor20132901 |
Volume: | 74 |
Issue: | 2 |
Start Page Number: | 181 |
End Page Number: | 217 |
Publication Date: | Jun 2013 |
Journal: | Queueing Systems |
Authors: | Miyazawa Masakiyo, Dai J |
Keywords: | Brownian motion |
We present three sets of results for the stationary distribution of a two‐dimensional semimartingale‐reflecting Brownian motion (SRBM) that lives in the non‐negative quadrant. The SRBM data can equivalently be specified by three geometric objects, an ellipse and two lines, in the two‐dimensional Euclidean space. First, we revisit the variational problem (VP) associated with the SRBM. Building on Avram et al. (2001), we show that the value of the VP at a point in the quadrant is equal to the optimal value of a linear function over a convex domain. Depending on the location of the point, the convex domain is either