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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 341, Pages 197–219 (Mi znsl145)  
Stochastic integral in case of infinite expectation of the first exit time

B. P. Harlamov

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences
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Abstract: A method of analysis of a multi-dimensional semi-Markov process of diffusion type in case of infinite expectation of the first exit time from a small neighborhood of the initial point is worked out. A generalization of a formula of Dynkin for this case is proved. The formula of Ito for the stochastic integral by the multi-dimensional semi-Markov process of diffusion type is derived.
Received: 20.11.2006
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 147, Issue 4, Pages 6962–6974
DOI: https://doi.org/10.1007/s10958-007-0522-6
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: B. P. Harlamov, “Stochastic integral in case of infinite expectation of the first exit time”, Probability and statistics. Part 11, Zap. Nauchn. Sem. POMI, 341, POMI, St. Petersburg, 2007, 197–219; J. Math. Sci. (N. Y.), 147:4 (2007), 6962–6974
Citation in format AMSBIB
\Bibitem{Har07}
\by B.~P.~Harlamov
\paper Stochastic integral in case of infinite expectation
of the first exit time
\inbook Probability and statistics. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 341
\pages 197--219
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl145}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2363596}
\zmath{https://zbmath.org/?q=an:1118.60072}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 147
\issue 4
\pages 6962--6974
\crossref{https://doi.org/10.1007/s10958-007-0522-6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36048948626}
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