Denisov, Denis; Sakhanenko, Alexander; Wachtel, Vitali First-passage times for random walks in the triangular array setting. (English) Zbl 1496.60041 Chaumont, Loïc (ed.) et al., A lifetime of excursions through random walks and Lévy processes. A volume in honour of Ron Doney’s 80th birthday. Cham: Birkhäuser. Prog. Probab. 78, 181-203 (2021). Summary: In this paper we continue our study of exit times for random walks with independent but not necessarily identically distributed increments. Our paper [Ann. Probab. 46, No. 6, 3313–3350 (2018; Zbl 1434.60126)] was devoted to the case when the random walk is constructed by a fixed sequence of independent random variables which satisfies the classical Lindeberg condition. Now we consider a more general situation when we have a triangular array of independent random variables. Our main assumption is that the entries of every row are uniformly bounded by a deterministic sequence, which tends to zero as the number of the row increases.For the entire collection see [Zbl 1478.60005]. Cited in 1 Document MSC: 60G50 Sums of independent random variables; random walks 60F17 Functional limit theorems; invariance principles 60G40 Stopping times; optimal stopping problems; gambling theory Keywords:random walk; triangular array; first-passage time; central limit theorem; moving boundary; transition phenomena Citations:Zbl 1434.60126 × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Arak, TV, On the distribution of the maximum of the succesive partial sums of independent random variables, Theory Probab Appl., 19, 245-266 (1975) · Zbl 0321.60044 · doi:10.1137/1119032 [2] Denisov, D.; Sakhanenko, A.; Wachtel, V., First-passage times for random walks with non-identically distributed increments, Ann. Probab., 46, 6, 3313-3350 (2018) · Zbl 1434.60126 · doi:10.1214/17-AOP1248 [3] Denisov, D., Sakhanenko, A., Wachtel, V.: First-passage times for random walks without Lindeberg condition. (2022) · Zbl 1434.60126 [4] Gaposhkin, VF, The law of the iterated logarithm for Cesaro’s and Abel’s methods of summation, Theory Probab. Appl., 10, 411-420 (1965) · doi:10.1137/1110049 [5] Tyurin, IS, Refinement of the upper bounds of the constants in Lyapunov’s theorem, Russian Math. Surv., 65, 3, 586-588 (2010) · Zbl 1225.60050 · doi:10.1070/RM2010v065n03ABEH004688 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.