We consider random walks with Gaussian distribution of summands. New representations for Wiener-Hopf factorization components are obtained. The factorization method is used to study the distribution of the excess over one-sided and two-sided boundaries. Asymptotic expansions for these distributions and for the expectation of the first exit time are obtained under the assumption that the boundaries tend to infinity.
"On some boundary crossing problems for Gaussian random walks." Ann. Probab. 24 (4) 2154 - 2171, October 1996. https://doi.org/10.1214/aop/1041903223