The Annals of Applied Probability

Finite Moments for Inventory Processes

Karl Sigman and David D. Yao

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 4, Number 3 (1994), 765-778.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004970

Digital Object Identifier
doi:10.1214/aoap/1177004970

Mathematical Reviews number (MathSciNet)
MR1284984

Zentralblatt MATH identifier
0817.60094

JSTOR
links.jstor.org

Subjects
Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 90B22: Queues and service [See also 60K25, 68M20]

Keywords
Reflection mapping finite moments stationary ergodic semimartingale queues

Citation

Sigman, Karl; Yao, David D. Finite Moments for Inventory Processes. Ann. Appl. Probab. 4 (1994), no. 3, 765--778. doi:10.1214/aoap/1177004970. https://projecteuclid.org/euclid.aoap/1177004970


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