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Zapiski Nauchnykh Seminarov POMI, 1997, Volume 244, Pages 96–118 (Mi znsl512)  

Equations for probability distributions of local time on surface for diffusion processes and control problems

N. G. Dokuchaev

St. Petersburg State University, Research Institute of Mathematics and Mechanics
Abstract: The paper studies local time on surface for general $n$-dimensional diffusion process. Analogs of Kolmogorov–Fokker–Planck equations for the characteristic function and probability distributions of local time are derived and investigated for a wide class of $(n-1)$-dimensional surfaces. A general explicit formula which is an analog of the Tanaka formula is presented. Optimal control problems with functionals which depend on local time are investigated.
Received: 02.11.1997
English version:
Journal of Mathematical Sciences (New York), 1997, Volume 99, Issue 2, Pages 1075–1088
DOI: https://doi.org/10.1007/BF02673628
Bibliographic databases:
UDC: 519.21
Language: Russian
Citation: N. G. Dokuchaev, “Equations for probability distributions of local time on surface for diffusion processes and control problems”, Probability and statistics. Part 2, Zap. Nauchn. Sem. POMI, 244, POMI, St. Petersburg, 1997, 96–118; J. Math. Sci. (New York), 99:2 (1997), 1075–1088
Citation in format AMSBIB
\Bibitem{Dok97}
\by N.~G.~Dokuchaev
\paper Equations for probability distributions of local time on surface for diffusion processes and control problems
\inbook Probability and statistics. Part~2
\serial Zap. Nauchn. Sem. POMI
\yr 1997
\vol 244
\pages 96--118
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl512}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1700382}
\zmath{https://zbmath.org/?q=an:0999.60501|0978.60501}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 99
\issue 2
\pages 1075--1088
\crossref{https://doi.org/10.1007/BF02673628}
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