Geodesic
Distributions of functionals of diffusions with jumps
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 15-36 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper deals with the generalization of diffusion with jumps. One of the main points is that the values of jumps depend on the position of the diffusion before the jump. The next generalization concerns the moments of jumps. They occur in accordance with the compound Poisson process or with the jumping moments constructed by the inverse integral functionals of the diffusion. 
@article{ZNSL_2006_339_a1,
     author = {A. N. Borodin},
     title = {Distributions of functionals of diffusions with jumps},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {15--36},
     year = {2006},
     volume = {339},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a1/}
}
TY  - JOUR
AU  - A. N. Borodin
TI  - Distributions of functionals of diffusions with jumps
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2006
SP  - 15
EP  - 36
VL  - 339
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a1/
LA  - ru
ID  - ZNSL_2006_339_a1
ER  - 
%0 Journal Article
%A A. N. Borodin
%T Distributions of functionals of diffusions with jumps
%J Zapiski Nauchnykh Seminarov POMI
%D 2006
%P 15-36
%V 339
%U http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a1/
%G ru
%F ZNSL_2006_339_a1
A. N. Borodin. Distributions of functionals of diffusions with jumps. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 15-36. http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a1/

[1] 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

[2] Girsanov I. V., “O preobrazovanii odnogo klassa sluchainykh protsessov s pomoschyu absolyutno nepreryvnoi zameny mery”, Teoriya veroyatn. i ee primen., 5:2 (1960), 314–330 | MR | Zbl

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

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

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

[6] Graham C., “Nonlinear diffusions with jumps”, Ann. Inst. Henri Poincaré (B), 28:3 (1992), 393–402 | MR | Zbl

[7] Borodin A. N., Ibragimov I. A., Predelnye teoremy dlya funktsionalov ot sluchainykh bluzhdanii, Trudy MIAN, 195, 1994 | MR | Zbl

[8] Borodin A. N., “O raspredelenii funktsionalov ot brounovskogo dvizheniya, ostanovlennogo v moment, obratnyi ko vremeni prebyvaniya”, Zap. nauchn. semin. POMI, 228, 1996, 39–56 | MR | Zbl