The Annals of Applied Probability

Finite Moments for Inventory Processes

Karl Sigman and David D. Yao

Full-text: Open access


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

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

First available in Project Euclid: 19 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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]

Reflection mapping finite moments stationary ergodic semimartingale queues


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

Export citation