The time until two renewal processes come together

W. Stadje

Statistics & Probability Letters, 1991, vol. 12, issue 3, 195-200

Abstract: Let (X0,j)j [greater-or-equal, slanted] 1 and (X1,j)j [greater-or-equal, slanted] 1 be two independent sequences of independent nonnegative random variables and let (S0,n)n [greater-or-equal, slanted] 1 and (S1,n)n [greater-or-equal, slanted] 1 be the corresponding renewal processes. For any positive number t let T(t) be the first time at which renewal points of the two processes are no more than t time units apart. It is shown that (under slight conditions) the boundedness of E(Xpi,j) implies the integrability of T(t)p-[delta] for any p > 1 and [delta] [epsilon] (0, p).

Date: 1991
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