Geodesic
Characteristic operator of a diffusion process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 226-251 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Characteristic operator of a~diffusion process},
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}
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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/

[1] A. N. Borodin, P. Salminen, Handbook of Brownian Motion – facts and Formulae, Birkhäuser Verlag, 1996 | MR | Zbl

[2] D. Gilbarg, N. Trudinger, Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl

[3] I. I. Gikhman, A. V. Skorokhod, Teoriya sluchainykh protsessov, tom I, Nauka, M., 1971 | MR

[4] E. B. Dynkin, Markovskie protsessy, Fizmatgiz, M., 1963 | MR | Zbl

[5] A. N. Kolmogorov, “Ob analiticheskikh metodakh v teorii veroyatnostei”, Uspekhi matem. nauk, 1938, no. 5, 5–41 | MR

[6] S. L. Sobolev, Uravneniya matematicheskoi fiziki, TTL, M., 1954 | MR

[7] B. P. Kharlamov, “Plotnost raspredeleniya tochki pervogo vykhoda diffuzionnogo protsessa iz maloi okrestnosti ego nachalnoi tochki”, Teoriya veroyatnostei i ee primeneniya, 45:3 (2000), 536–554, Nauka, M. | MR

[8] B. P. Kharlamov, Nepreryvnye polumarkovskie protsessy, Nauka, SPb, 2001 | MR

[9] B. P. Kharlamov, “Absolyutnaya nepreryvnost mer v klasse polumarkovskikh protsessov diffuzionnogo tipa”, Zap. nauchn. semin. POMI, 294, 2002, 216–244 | MR | Zbl