THE TIME UNTIL 2 RENEWAL PROCESSES COME TOGETHER

Abstract

Let (X0,j)j greater-than-or-equal-to 1 and (X1,j)j greater-than-or-equal-to 1 be two independent sequences of independent nonnegative random variables and let (S0,n) n greater-than-or-equal-to 1 and (S1,n)n greater-than-or-equal-to 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(X(i,j)p,) implies the integrability of T(t)p-delta for any p > 1 and delta element-of (0, p).