标题： 具有中间阶扰动的随机游走的非线性更新定理 显示英文标题

标题： Nonlinear renewal theorems for random walks with perturbations of intermediate order

摘要： 我们为一种扰动随机游走发展非线性更新定理，而无需假设中心扰动项的随机有界性。 通过某些线性和非线性停止规则之间的差的均匀可积性，获得了期望停止时间的二阶展开式。 得到一个中间更新定理，该定理提供了非线性版本的基本和常规更新定理之间的展开式。 两个样本秩序概率比检验的期望样本量被作为激励例子进行考虑。 显示英文摘要

摘要： We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of the difference between certain linear and nonlinear stopping rules. An intermediate renewal theorem is obtained which provides expansions between the nonlinear versions of the elementary and regular renewal theorems. The expected sample size of a two-sample rank sequential probability ratio test is considered as the motivating example.