Geodesic
Limiting distribution of the exit time out of an expanding interval and of the position at this moment of a~process with independent increments and one-signed jumps
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 419-425

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Let $\xi(t)$ be a process with independent increments and negative jumps starting from a point $x\in(0,T)$ and let $\tau_T$ be the exit time out of the interval $(0,T)$. The limiting distribution (as $T\to\infty$) of the pair $(\tau_T/T^2,\xi(\tau_T))$ is found. 
@article{TVP_1978_23_2_a18,
     author = {V. M. \v{S}urenkov},
     title = {Limiting distribution of the exit time out of an expanding interval and of the position at this moment of a~process with independent increments and one-signed jumps},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {419--425},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a18/}
}
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V. M. Šurenkov. Limiting distribution of the exit time out of an expanding interval and of the position at this moment of a~process with independent increments and one-signed jumps. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 419-425. http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a18/