Geodesic
On the distribution of the first jump over a~high barrier for a~generalized Poisson process with drift
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 159-163

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Let $\xi(t)$ be a process with independent increments and finite number of jumps. Define $\eta_x=\inf\{t\colon\xi(t)\ge x\}$ and $\chi_x=\xi(\eta_x)-x(x>0)$. For the limit distribution $$ \lim_{x\to\infty}\mathbf P\{\chi_x\le x\} $$ explicit expresions are given. 
@article{TVP_1974_19_1_a13,
     author = {A. I. Fokht},
     title = {On the distribution of the first jump over a~high barrier for a~generalized {Poisson} process with drift},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {159--163},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a13/}
}
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A. I. Fokht. On the distribution of the first jump over a~high barrier for a~generalized Poisson process with drift. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 1, pp. 159-163. http://geodesic.mathdoc.fr/item/TVP_1974_19_1_a13/