The exponential moment tail of inhomogeneous renewal process

Emilija Bernackaitė and Jonas Šiaulys

Statistics & Probability Letters, 2015, vol. 97, issue C, 9-15

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.

Keywords: Inhomogeneous renewal process; Exponential estimate; Renewal theorem (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2014.10.018

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