Geodesic
Martingales and first passage times for Ornstein--Uhlenbeck processes with a jump component
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 2, pp. 340-358

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Using martingale technique, we show that a distribution of the first-passage time over a level for the Ornstein–Uhlenbeck process with jumps is exponentially bounded. In the case of absence of positive jumps, the Laplace transform for this passage time is found. Further, the maximal inequalities are also given when the marginal distribution is stable.
Keywords: exponential martingales, first-passage times, Ornstein–Uhlenbeck process, moment Wald's identity, maximal inequalities
Mots-clés : Laplace transform, stable distribution. 
@article{TVP_2003_48_2_a6,
     author = {A. A. Novikov},
     title = {Martingales and first passage times for {Ornstein--Uhlenbeck} processes with a jump component},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {340--358},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_2_a6/}
}
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A. A. Novikov. Martingales and first passage times for Ornstein--Uhlenbeck processes with a jump component. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 2, pp. 340-358. http://geodesic.mathdoc.fr/item/TVP_2003_48_2_a6/