Optimal paths in large deviations of symmetric reflected Brownian motion in the octant - Ziyu Liang; John J. Hasenbein (Stochastic Systems, 2013)
We study the variational problem that arises from considerationof large deviations for semimartingale reflected Brownian motion (SRBM) in $mathbbR^3_+$. Due to the difficulty of the general problem,we consider the case in which the SRBM has rotationallysymmetric parameters. In this case, we are able to obtain conditionsunder which the optimal solutions to the variational problem arepaths that are gradual (moving through faces of strictly increasingdimension) or that spiral around the boundary of the octant.Furthermore, these results allow us to provide an example for whichit can be verified that a spiral path is optimal. For rotationally symmetric SRBM's, our results facilitate the simplification of computational methodsfor determining optimal solutions to variational problems and give insightinto large deviations behavior of these processes.