Let & be a persistent aperiodic recurrent event. Assume that the re- currence time has finite mean
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Let & be a persistent aperiodic recurrent event. Assume that the re- currence time has finite mean and variance 02.
Put qn = fn+1 + fn +2 +.. and r9n+1+9+2 + Show that the generating functions Q(s) and R(s) converge for s = 1.
Prove that R(s) Q(s) (un - 11) 5 = 10(5) (12.1) and hence that (12.2) (-) - ==== 22
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Related Book For 
An Introduction To Probability Theory And Its Applications Volume 1
ISBN: 9780471257110
3rd Edition
Authors: William Feller
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