Affiliation:
1. Faculté des Sciences Juridiques, Économiques et sociales, Ain Sebaa., Université Hassan II de Casablanca, Casablanca, Morocco
Abstract
AbstractSemimartingale reflecting Brownian motions (SRBMs) are diffusion processes, which arise as approximations for open d-station queueing networks of various kinds. The data for such a process are a drift vector θ, a nonsingular {d\times d} covariance matrix Δ, and a {d\times d} reflection matrix R. The state space is the d-dimensional nonnegative orthant, in the interior of which the processes evolve according to a Brownian motions, and that reflect against the boundary in a specified manner.
A standard problem is to determine under what conditions the process is positive recurrent. Necessary and sufficient conditions are formulated for some classes of reflection matrices and in two- and three-dimensional cases, but not more.
In this work, we identify a new family of reflection matrices R for which the process is positive recurrent if and only if the drift {\theta\in\mathring{\Gamma}}, where {\mathring{\Gamma}} is the interior of the convex wedge generated by the opposite column vectors of R.
Subject
Statistics and Probability,Analysis