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The exponential moment tail of inhomogeneous renewal process

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  • Bernackaitė, Emilija
  • Šiaulys, Jonas

Abstract

Let θ1,θ2,… be a sequence of nonnegative not necessarily identically distributed and independent random variables having finite means and satisfying some additional conditions. We consider the asymptotic behavior of the quantity E(bΘ(t)1Θ(t)>at), where a and b are suitable positive constants, and Θ(t) is an inhomogeneous renewal process generated by the sequence θ1,θ2,…. We also present a few corollaries concerning elementary renewal theorems for the above process.

Suggested Citation

  • Bernackaitė, Emilija & Šiaulys, Jonas, 2015. "The exponential moment tail of inhomogeneous renewal process," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 9-15.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:9-15
    DOI: 10.1016/j.spl.2014.10.018
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    References listed on IDEAS

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    1. Chen, Yiqing & Yuen, Kam C., 2012. "Precise large deviations of aggregate claims in a size-dependent renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 457-461.
    2. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    3. Tang, Qihe & Su, Chun & Jiang, Tao & Zhang, Jinsong, 2001. "Large deviations for heavy-tailed random sums in compound renewal model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 91-100, March.
    4. Lu, Dawei, 2011. "Lower and upper bounds of large deviation for sums of subexponential claims in a multi-risk model," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1911-1919.
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    1. Edita Kizinevič & Jonas Šiaulys, 2018. "The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model," Risks, MDPI, vol. 6(1), pages 1-17, March.

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