Abstract
Renewal theory is developed for processes of the form $Z_n = S_n + \xi_n$, 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 $\mu$ and $\xi_n$ is independent of $X_{n+1}, X_{n+2}, \cdots$ and has sample paths which are slowly changing in an appropriate sense. Applications to sequential analysis are given.
Citation
T. L. Lai. D. Siegmund. "A Nonlinear Renewal Theory with Applications to Sequential Analysis I." Ann. Statist. 5 (5) 946 - 954, September, 1977. https://doi.org/10.1214/aos/1176343950
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