Geodesic
Transformations of diffusions with jumps
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 79-100 
A. N. Borodin. Transformations of diffusions with jumps. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 12, Tome 351 (2007), pp. 79-100. http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a3/
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     author = {A. N. Borodin},
     title = {Transformations of diffusions with jumps},
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     year = {2007},
     volume = {351},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_351_a3/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper deals with some transformations of diffusions with jumps. We consider the class of diffusions with jumps which is closed with respect to the composition with invertable twice continuously differentiable functions. The special randon time change leads again to the diffusion with jumps. The result concerning a transformation of the measure is valid to this class of diffusions with jumps.

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

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

[4] 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

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

[6] Borodin A. N., “Raspredelenie funktsionalov ot skachkoobraznykh diffuzii”, Zap. nauchn. semin. POMI, 339, 2005, 15–36 | MR