Several Properties of a Nonstandard Renewal Counting Process and Their Applications

This paper proposes a nonstandard renewal counting process based on web Markov skeleton process, called web renewal process, which allows applications in the field of natural science and social science. Parallel with the standard renewal counting process, some properties of the web renewal process a...

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Bibliographic Details
Published in:Journal of systems science and complexity 2020-02, Vol.33 (1), p.122-136
Main Authors: Li, Rong, Bi, Xiuchun, Zhang, Shuguang
Format: Article
Language:English
Subjects:
Complex Systems
Control
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Properties (attributes)
Renewals
Statistics
Systems Theory
Webs
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Summary:This paper proposes a nonstandard renewal counting process based on web Markov skeleton process, called web renewal process, which allows applications in the field of natural science and social science. Parallel with the standard renewal counting process, some properties of the web renewal process and the corresponding web renewal reward processes, are investigated. Several limit properties, including the tail of the exponential moments of the web renewal process, and the results of precise large deviations and moderate deviations for the web renewal reward processes are derived.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-019-8159-3