Sums of Identically Distributed Renewal Processes. Suppose that N˜1, N˜2 ... are independent renewal processes with inter-renewal distribution F. By the strong law of large numbers, we know that the...

Sums of Identically Distributed Renewal Processes. Suppose that N˜1, N˜2 ... are independent renewal processes with inter-renewal distribution F. By the strong law of large numbers, we know that the sum onverges to ∞ a.s. as n → ∞. (The discussion prior to Example 65 addressed the opposite case where the sum tends to 0.) To normalize this sum (analogously to that in a central limit theorem) so that it converges to a non-degenerate limitExample 65