On some boundary crossing problems for Gaussian random walks (Q674526)

The author considers the Gaussian random walks and obtains for them some new representations of the Wiener-Hopf factorization components as well as the asymptotic expansions for the distribution of the excess over one-sided and two-sided boundaries. For related papers see \textit{A. A. Borovkov} [Select. Transl. Math. Stat. Probab. 5, 315-372 (1965); translation from Sib. Mat. Zh. 3, 645-694 (1962; Zbl 0128.12906)], \textit{B. A. Rogozin} [Sib. Math. J. 10(1969), 989-1010 (1970); translation from Sib. Mat. Zh. 10, 1334-1363 (1969; Zbl 0184.40602)], \textit{Eh. L. Presman} [Math. USSR, Izv. 3(1969), 815-852 (1970); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 33, 861-900 (1969; Zbl 0192.55102)], and \textit{V. I. Lotov} [Theory Probab. Appl. 32, 57-67 (1987); translation from Teor. Veroyatn. Primen. 32, No. 1, 62-72 (1987; Zbl 0622.62081)].