Geodesic
On distributions of passage times of Brownian motion with jumps
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 101-116 
A. N. Borodin. On distributions of passage times of Brownian motion with jumps. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 101-116. http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a4/
@article{ZNSL_2007_351_a4,
     author = {A. N. Borodin},
     title = {On distributions of passage times of {Brownian} motion with jumps},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {101--116},
     year = {2007},
     volume = {351},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Brownian motion with jumps that is the sum of Brownian motion and compound Poisson process is considered. It is assumed that the distribution of jumps is symmetric exponential. The formula for the Laplace transform of the distribution of time spend by Brownian motion with jumps upper than some level is obtained.

[1] Lévy P., “Sur certains processus stochatiques homogènes”, Compositio Math., 7:2 (1939), 283–339 | MR

[2] Kac M., “On distribution of certain Wiener functionals”, Trans. Amer. Math. Soc., 65:1 (1949), 1–13 | DOI | MR | Zbl

[3] Kac M., “On some connections between probability theory and differential and integral equations”, Proc. Second Berkley Symp. Math. Stat. Probab. (1951), 189–215 | MR | Zbl

[4] Skorokhod A. V., Sluchainye protsessy s nezavisimymi prirascheniyami, Nauka, M., 1964 | MR | Zbl

[5] Mordecki E., “Ruin probabilities for Lévy processes with mixed exponential negative jumps”, Teoriya veroyatn. i ee primen., 48:1 (2003), 188–194 | MR | Zbl

[6] Borodin A. N., “Raspredelenie funktsionalov ot nekotorykh protsessov s nezavisimymi prirascheniyami”, Vestnik SPbGU. Ser. 1, 2005, no. 4, 7–20 | MR

[7] Borodin A. N., “Raspredelenie funktsionalov ot skachkoobraznogo diffuzionnogo protsessa”, Zap. nauchn. semin. POMI, 328, 2005, 27–41 | MR | Zbl

[8] Borodin A.N., Salminen P., Handbook of Brownian Motion – Facts and Formulae, Second edition, Birkhäuser, Basel–Boston–Berlin, 2002 | MR | Zbl