Geodesic
Distributions of functionals of diffusions with jumps
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 10, Tome 339 (2006), pp. 15-36

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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},
     publisher = {mathdoc},
     volume = {339},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_339_a1/}
}
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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/