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Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-43, 43 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-09-22
Country of Publication
Egypt
No. of Pages
43
Main Subjects
Abstract EN
The class of counting processes constitutes a significant part of applied probability.
The classic counting processes include Poisson processes, nonhomogeneous Poisson processes, and renewal processes.
More sophisticated counting processes, including Markov renewal processes, Markov modulated Poisson processes, age-dependent counting processes, and the like, have been developed for accommodating a wider range of applications.
These counting processes seem to be quite different on the surface, forcing one to understand each of them separately.
The purpose of this paper is to develop a unified multivariate counting process, enabling one to express all of the above examples using its components, and to introduce new counting processes.
The dynamic behavior of the unified multivariate counting process is analyzed, and its asymptotic behavior as t→∞ is established.
As an application, a manufacturing system with certain maintenance policies is considered, where the optimal maintenance policy for minimizing the total cost is obtained numerically.
American Psychological Association (APA)
Sumita, Ushio& Huang, Jia-Ping. 2009. Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-43.
https://search.emarefa.net/detail/BIM-455615
Modern Language Association (MLA)
Sumita, Ushio& Huang, Jia-Ping. Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-43.
https://search.emarefa.net/detail/BIM-455615
American Medical Association (AMA)
Sumita, Ushio& Huang, Jia-Ping. Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-43.
https://search.emarefa.net/detail/BIM-455615
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-455615