Geodesic
The distribution of the first hit for stable and asymptotically stable walks on an interval
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 2, pp. 342-349

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Let $\{\xi(t);t\ge0\}$ be a strongly stable process, $\tau=\inf\{t\colon\xi(t)\notin[0,1]\}$. Formulas for $\mathbf P\{1\le\xi(\tau)1+y\mid\xi(0)=x\}$, and $\mathbf P\{0\ge\xi(\tau)>-y\mid\xi(0)=x\}$, $0\le x\le1$, $y\ge0$, are derived and applied to random walks. 
@article{TVP_1972_17_2_a9,
     author = {B. A. Rogozin},
     title = {The distribution of the first hit for stable and asymptotically stable walks on an interval},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {342--349},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a9/}
}
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B. A. Rogozin. The distribution of the first hit for stable and asymptotically stable walks on an interval. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 2, pp. 342-349. http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a9/