Abstract
This paper continues earlier work of the authors. An analogue of Blackwell's renewal theorem is obtained for processes $Z_n = S_n + \xi_n$, where $S_n$ is the $n$th partial sum of a sequence $X_1, X_2, \cdots$ of independent identically distributed random variables with finite positive mean and $\xi_n$ is independent of $X_{n+1}, X_{n+2}, \cdots$ 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.
Citation
T. L. Lai. D. Siegmund. "A Nonlinear Renewal Theory with Applications to Sequential Analysis II." Ann. Statist. 7 (1) 60 - 76, January, 1979. https://doi.org/10.1214/aos/1176344555
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