Approximations to expected stopping times with applications to sequential estimation

Abstract

In this paper we consider sharp asymptotic aproximations to renewal functions associated with general stochastic sequences. We establish a variant of Smith's renewal theorem with a bounded remainder term imposing moment conditions on the underlying stochastic sequence. This result is then applied to an asymptotic analysis of stopping times arising in sequential estimation problems. We show that the renewal theorem can be used for deriving approximations to the expected values of first passage times for random walks with dependent increments