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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 431, Pages 209–241
(Mi znsl6104)
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This article is cited in 2 scientific papers (total in 2 papers)
Final distribution of a diffusion process with a final stop
B. P. Harlamov Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
One-dimensional diffusion process is considered. A characteristic operator of this process is assumed to be a linear differential operator of the second order with a negative coefficient in the operator's member without derivative. Such an operator determines a measure of a Markov diffusion process with a break (the first interpretation), and also that of a semi-Markov diffusion process with a final stop (the second interpretation). Under the second interpretation the existence of a limit on infinity of the process (the final point) is characterized. This limit exists on any interval almost sure with respect to a conditional measure, generated by condition that the process never leaves this interval. A distribution of the final point expressed in terms of two fundamental solutions of the corresponding ordinary differential equation, and also that of the final stop beginning instant are derived. A homogeneous process is considered as an example.
Key words and phrases:
Markov process, continuous semi-Markov process, Markov moment, first exit time, final point, density of final distribution.
Received: 16.09.2014
Citation:
B. P. Harlamov, “Final distribution of a diffusion process with a final stop”, Probability and statistics. Part 21, Zap. Nauchn. Sem. POMI, 431, POMI, St. Petersburg, 2014, 209–241; J. Math. Sci. (N. Y.), 214:4 (2016), 562–583
Linking options:
https://www.mathnet.ru/eng/znsl6104 https://www.mathnet.ru/eng/znsl/v431/p209
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Abstract page: | 134 | Full-text PDF : | 32 | References: | 30 |
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