A Nonlinear Renewal Theory with Applications to Sequential Analysis II

Abstract : An analogue of Blackwell's renewal theorem is obtained for processes Z sub n = S sub n + xi sub n, where S sub n is the nth partial sum of a sequence X1,X2,... of independent identically distributed random variables with finite positive mean and xi sub n is independent of X sub n+1, X sub n+2,.. and has sample paths which are slowly changing in a sense made precise below. As a consequence, asymptotic expansions up to terms tending to 0 are obtained for the expected value of certain first passage times. Applications to sequential analysis are given.