Geodesic
The distribution of the size of the first jump over a~level for a~class of stochastic processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 430-434

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The paper deals with a stochastic process with independent increments with the characteristic function $$ \varphi(t,z)=\exp\biggl\{t\biggl[i\alpha z-\frac{\sigma^2}{2}z^2+\lambda\int_0^{\infty}(e^{izx}-1)F\,(dx)\biggr]\biggr\}. $$ For the distribution of the size of the first jump over a level $x>0$, a) an integro-differential equation (in $x$) is obtained, b) the limiting behaviour is studied as $x\to\infty$ and c) the Laplace transform (in $x$) is found. 
@article{TVP_1976_21_2_a23,
     author = {A. I. Foht},
     title = {The distribution of the size of the first jump over a~level for a~class of stochastic processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {430--434},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a23/}
}
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A. I. Foht. The distribution of the size of the first jump over a~level for a~class of stochastic processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 430-434. http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a23/