Geodesic
On estimates and the asymptotic behavior of nonexit probabilities of a~Wiener process to a~moving boundary
Sbornik. Mathematics, Tome 38 (1981) no. 4, pp. 495-505

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In this paper the asymptotic behavior, as well as upper and lower bounds, is found for the probabilities $\mathsf P\{\sigma>T\}=\mathsf P\{|w_t|\leqslant f(t),0\leqslant t\leqslant T\}$, $\mathsf P\{\sigma>T\}=\mathsf P\{w_t\geqslant g(t),0\leqslant t\leqslant T\}$ for large classes of functions $f$ and $g$. Bibliography: 21 titles. 
@article{SM_1981_38_4_a3,
     author = {A. A. Novikov},
     title = {On estimates and the asymptotic behavior of nonexit probabilities of {a~Wiener} process to a~moving boundary},
     journal = {Sbornik. Mathematics},
     pages = {495--505},
     publisher = {mathdoc},
     volume = {38},
     number = {4},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_38_4_a3/}
}
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A. A. Novikov. On estimates and the asymptotic behavior of nonexit probabilities of a~Wiener process to a~moving boundary. Sbornik. Mathematics, Tome 38 (1981) no. 4, pp. 495-505. http://geodesic.mathdoc.fr/item/SM_1981_38_4_a3/