Geodesic
Distributions of functionals of diffusions with jumps
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 27-41 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper deals with methods of computation of distributions of functionals of a diffusion process with jumps that occur in accordance with the compound Poisson process. For symmetric processes some exact formulae concerning the first exit time are derived. 
@article{ZNSL_2005_328_a2,
     author = {A. N. Borodin},
     title = {Distributions of functionals of diffusions with jumps},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {27--41},
     year = {2005},
     volume = {328},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a2/}
}
TY  - JOUR
AU  - A. N. Borodin
TI  - Distributions of functionals of diffusions with jumps
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 27
EP  - 41
VL  - 328
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a2/
LA  - ru
ID  - ZNSL_2005_328_a2
ER  - 
%0 Journal Article
%A A. N. Borodin
%T Distributions of functionals of diffusions with jumps
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 27-41
%V 328
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a2/
%G ru
%F ZNSL_2005_328_a2
A. N. Borodin. Distributions of functionals of diffusions with jumps. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 27-41. http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a2/

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

[2] 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

[3] Baxter G., Donsker M. D., “On distribution of the supremum functionals for processes with stationary independent increments”, Trans. Amer. Math. Soc., 85:1 (1957), 73–87 | DOI | MR | Zbl

[4] Skorokhod A. V., Sluchainye protsessy s nezavisimymi prirascheniyami, M., 1964

[5] Zolotarev V. M., “Moment pervogo prokhozhdeniya urovnya i povedenie na beskonechnosti odnogo klassa protsessov s nezavisimymi prirascheniyami”, Teoriya veroyatn. i ee primen., 9:4 (1964), 724–733 | MR | Zbl

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