Lotov, V. I. Asymptotic expansions for the CUSUM procedure in a change point problem. (English) Zbl 0848.60041 Sib. Adv. Math. 2, No. 3, 158-172 (1992). Summary: Let \(\{\xi_n\}\) be a sequence of i.i.d. random variables, \(N = \min \{n \geq 1 : \xi_1 + \cdots + \xi_n \notin [0,b)\}\). Asymptotic expansions at \(b\to\infty\) are obtained for the distribution and expectation of \(S_N\) under Cramér type conditions. These results are applied to the study of asymptotic properties of the CUSUM procedure in a change point problem. MSC: 60F99 Limit theorems in probability theory 62E10 Characterization and structure theory of statistical distributions 60G50 Sums of independent random variables; random walks Keywords:change point problem; CUSUM procedure; random walk with two barriers; factorization method PDFBibTeX XMLCite \textit{V. I. Lotov}, Sib. Adv. Math. 2, No. 3, 158--172 (1992; Zbl 0848.60041)