Geodesic
Asymptotics for the probability of not exceeding a curvilinear level by a Gaussian random walk
Izvestiya. Mathematics , Tome 73 (2009) no. 1, pp. 47-77

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We get a correction term in the asymptotics for the probability of not exceeding a curvilinear level by a trajectory of a Gaussian random walk. We also estimate the density of distribution of the maxima of some Gaussian processes.
Keywords: boundary value problem, random walk. 
@article{IM2_2009_73_1_a4,
     author = {N. K. Bakirov},
     title = {Asymptotics for the probability of not exceeding a curvilinear level by a {Gaussian} random walk},
     journal = {Izvestiya. Mathematics },
     pages = {47--77},
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     volume = {73},
     number = {1},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_1_a4/}
}
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N. K. Bakirov. Asymptotics for the probability of not exceeding a curvilinear level by a Gaussian random walk. Izvestiya. Mathematics , Tome 73 (2009) no. 1, pp. 47-77. http://geodesic.mathdoc.fr/item/IM2_2009_73_1_a4/