Abstract
Let $T$ be the first time that a perturbed random walk crosses a nonlinear boundary. This paper concerns the approximations of the distribution of the excess over the boundary, the expected stopping time $ET$ and the variance of the stopping time $\operatorname{Var}(T)$. Expansions are obtained by using linear renewal theorems with varying drift.
Citation
Cun-Hui Zhang. "A Nonlinear Renewal Theory." Ann. Probab. 16 (2) 793 - 824, April, 1988. https://doi.org/10.1214/aop/1176991788
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