The asymptotic joint distribution of the state occupancy times in an alternating renewal process

J. E. Angus

Naval Research Logistics Quarterly, 1986, vol. 33, issue 3, 385-390

Abstract: An alternating renewal process starts at time zero and visits states 1,2,…,r, 1,2, …,r 1,2, …,r, … in sucession. The time spent in state i during any cycle has cumulative distribution function Fi, and the sojourn times in each state are mutually independent, positive and nondegenerate random variables. In the fixed time interval [0,T], let Ui(T) denote the total amount of time spent in state i. In this note, a central limit theorem is proved for the random vector (Ui(T), 1 ≤ i ≤ r) (properly normed and centered) as T → ∞.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:33:y:1986:i:3:p:385-390

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