A NEW REPRESENTATION FOR A RENEWAL-THEORETIC CONSTANT APPEARING IN ASYMPTOTIC APPROXIMATIONS OF LARGE DEVIATIONS

The probability that a stochastic process with negative drift exceed a value a often has a renewal-theoretic approximation as a --> infinity . Except for a process of iid random variables, this approximation inv olves a constant which is not amenable to analytic calculation. Naive simulation of this constant has the drawback of necessitating a choice of finite a, thereby hurting assessment of the precision of a Monte C arlo simulation estimate, as the effect of the discrepancy between a a nd infinity is usually difficult to evaluate. Here we suggest a new wa y of representing the constant. Our approach enables simulation of the constant with prescribed accuracy. We exemplify our approach by worki ng out the details of a sequential power one hypothesis testing proble m of whether a sequence of observations is lid standard normal against the alternative that the sequence is AR(1). Monte Carlo results are r eported.