|Stability Properties for Constrained Jump Diffusion Processes
Department of Statistics
University of North Carolina
Monday, October 31, 2005
E203 Engineering Building
We consider a class of jump-diffusion processes that are constrained to take values in a polyhedral cone. Processes of this type arise in the heavy traffic analysis of multiclass queuing networks. Sufficient conditions for positive recurrence and transience of this class of Markov processes are presented. Under suitable conditions we establish geometric ergodicity and as a consequence obtain several desirable properties of the Markov process, such as, stability of moments, finite exponential moments for the invariant measure, functional central limit theorems, etc.