Geodesic
Characteristic operator of a diffusion process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 226-251 
B. P. Harlamov. Characteristic operator of a diffusion process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 226-251. http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a14/
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     author = {B. P. Harlamov},
     title = {Characteristic operator of a~diffusion process},
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     year = {2003},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a14/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Semi-Markov processes of diffusion type in the $d$-dimensional space ($d\geq1$) are considered. The transition generating function of such a process is assumed to satisfy the second order differential equation of elliptical type. Using methods of differential equation theory, especially that of Dirichlet problem, the transition generating function for a small neighborhood of the initial point of the process is investigated. The asymptotic expansions on a small scale parameter are obtained both for the first exit point distribution density, and for the first exit time expectation, when the trajectory of the process leaves a small neighborhood of the initial point. The characteristic operator of E. B. Dynkin determined by a decreasing sequence of neighborhoods is proved to exist.

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