|
Zapiski Nauchnykh Seminarov POMI, 2003, Volume 298, Pages 226–251
(Mi znsl1174)
|
|
|
|
This article is cited in 2 scientific papers (total in 2 papers)
Characteristic operator of a diffusion process
B. P. Harlamov Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
Abstract:
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.
Received: 12.07.2003
Citation:
B. P. Harlamov, “Characteristic operator of a diffusion process”, Probability and statistics. Part 6, Zap. Nauchn. Sem. POMI, 298, POMI, St. Petersburg, 2003, 226–251; J. Math. Sci. (N. Y.), 128:1 (2005), 2625–2639
Linking options:
https://www.mathnet.ru/eng/znsl1174 https://www.mathnet.ru/eng/znsl/v298/p226
|
Statistics & downloads: |
Abstract page: | 281 | Full-text PDF : | 61 | References: | 46 |
|