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

✍ Scribed by J. E. Angus

• Publisher: John Wiley and Sons
• Year: 1986
• Tongue: English
• Weight: 264 KB
• Volume: 33
• Category: Article
• ISSN: 0894-069X
• DOI: 10.1002/nav.3800330304

✦ Synopsis

An alternating renewal process starts at time zero and visits states 1,2, . . . ,r, 1,2, . . . ,r, 1,2, . . . ,r, . . . in succession. The time spent in state i during any cycle has cumulative distribution function F,, and the sojourn times in each state are mutually independent, positive and nondegenerate random variables. In the fixed time interval [O,q, let U,(T) denote the total amount of time spent in state i. In this note, a central limit theorem is proved for the random vector (U,(T), 1 I i I r ) (properly normed and centered) as 7' + 00.