Finite moments for inventory processes
type: Item
instance of: scholarly article
title: Finite moments for inventory processes
zbMATH Open document ID: 0817.60094
author: Karl Sigman
author: David D. Yao
published in: The Annals of Applied Probability
publication date: 1995-07-17T00:00:00Z
review text: Let \(\{Z(t),\;t \geq 0\}\) be a continuous time inventory process which is a reflection mapping of a netput process \(\{X(t), t \geq 0\}\) with negative drift and \(X(0) = 0\). In other words \(Z(t) = X(t) + L(t)\), where \(L(t) = \sup_{0 \leq s \leq t} X^ -(s)\) with \(X^ -(s) = - \min (0, X(s))\). Processes of this type include workload process in queues and storage level in dam problems. The authors establish sufficient conditions on the netput which ensures the steady state inventory to have finite moments of order \(k \geq 1\) and obtain explicit bounds for these moments. The results are presented in detail, with examples, for the case when the netput has a bounded variation and are extended to the semi- martingale case.
Mathematics Subject Classification ID: 60K30
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 681401
zbMATH Keywords: finite moments
zbMATH Keywords: single server queues
zbMATH Keywords: reflection mapping
zbMATH Keywords: steady state inventory
zbMATH Keywords: bounded variation
zbMATH Keywords: semi-martingale
reviewed by: S. Kalpakam
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177004970
OpenAlex ID: W2053217728
DOI: 10.1214/AOAP/1177004970
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description: scientific article; zbMATH DE number 681401