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August, 1994 Finite Moments for Inventory Processes
Karl Sigman, David D. Yao
Ann. Appl. Probab. 4(3): 765-778 (August, 1994). DOI: 10.1214/aoap/1177004970


We study a continuous time inventory process that is a reflection mapping of a semimartingale netput process. Inventory processes of this type include the workload process in queues, dam and storage processes (with perhaps pure jump Levy input), as well as processes arising in fluid models. We establish sufficient conditions on the netput ensuring that the steady-state inventory has finite moments of order $k \geq 1$, and derive explicit bounds for these moments. The sufficient conditions require that the netput have a negative (local) drift and that the (conditional) $(k + 1)$th moment of its increments be bounded.


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Karl Sigman. David D. Yao. "Finite Moments for Inventory Processes." Ann. Appl. Probab. 4 (3) 765 - 778, August, 1994.


Published: August, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0817.60094
MathSciNet: MR1284984
Digital Object Identifier: 10.1214/aoap/1177004970

Primary: 60K30
Secondary: 60K25 , 90B22

Keywords: finite moments , queues , Reflection mapping , Semimartingale , stationary ergodic

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.4 • No. 3 • August, 1994
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