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Several Properties of a Nonstandard Renewal Counting Process and Their Applications

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Abstract

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.

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Authors and Affiliations

  1. Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, 233030, China

    Rong Li & Xiuchun Bi

  2. Department of Statistics and Finance, University of Science and Technology of China, Hefei, 230022, China

    Rong Li, Xiuchun Bi & Shuguang Zhang

Authors
  1. Rong Li
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  2. Xiuchun Bi
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  3. Shuguang Zhang
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Corresponding authors

Correspondence to Rong Li, Xiuchun Bi or Shuguang Zhang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11401556 and 11471304.

This paper was recommended for publication by Editor WANG Shouyang.

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Li, R., Bi, X. & Zhang, S. Several Properties of a Nonstandard Renewal Counting Process and Their Applications. J Syst Sci Complex 33, 122–136 (2020). https://doi.org/10.1007/s11424-019-8159-3

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  • DOI: https://doi.org/10.1007/s11424-019-8159-3

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