Asymptotic distribution of rewards accumulated by alternating renewal processes

Patrick Chisan Hew

Statistics & Probability Letters, 2017, vol. 129, issue C, 355-359

Abstract: Consider an alternating renewal process on the states ‘broken’ vs ‘working’. Suppose that during any interval [0,τ], the process is rewarded at rate g(t∕τ) if it is working at time t. Let Qτ be the reward that is accumulated during [0,τ]. We calculate μQτ and σQτ2 such that (Qτ−μQτ)∕σQτ converges in distribution to a standard normal distribution as τ→∞.

Keywords: Reward; Alternating renewal process; Asymptotically normal (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.06.027

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