RECURRENCE CLASSIFICATION FOR A FAMILY OF NON-LINEAR
STORAGE MODELS
Peter W. Glynn
John E. Glynn
Sanatan Rai
Abstract: Necessary and sufficient conditions for positive recurrence of a
discrete-time non-linear storage model with power law dynamics are
derived. In addition, necessary and sufficient conditions for finiteness of
-th stationary moments are obtained for this class of models.
2010 AMS Mathematics Subject Classification: Primary: 60J05; Secondary:
60J20.
Keywords and phrases: Markov chains, storage theory, positive recurrence, Lyapunov
functions.