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Teor. Veroyatnost. i Primenen., 1968, Volume 13, Issue 4, Pages 602–620 (Mi tvp896)  

Nonlinear interpolation of components of diffusion Markov processes

R. Sh. Liptser, A. N. Shiryaev

Moscow

Abstract: A diffusion Markov process defined by the Ito equations (3) is considered. For the a posteriori probability densities $\pi_{\alpha\beta}(t,\tau)$, $\pi_\alpha(t,\tau)$, $0\le t\le\tau\le T$ defined in (2), differential equations in $\tau$ are deduced (see (21) and (13)). In §2 for the coefficients (31), it is shown that $\pi_\alpha(t,\tau)$ and $\pi_{\alpha\beta}(t,\tau)$ are Gaussian densities in $\alpha$ with parameters defined by (37), (38) and (65), (66).

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English version:
Theory of Probability and its Applications, 1968, 13:4, 564–583

Bibliographic databases:

Received: 27.12.1967

Citation: R. Sh. Liptser, A. N. Shiryaev, “Nonlinear interpolation of components of diffusion Markov processes”, Teor. Veroyatnost. i Primenen., 13:4 (1968), 602–620; Theory Probab. Appl., 13:4 (1968), 564–583

Citation in format AMSBIB
\Bibitem{LipShi68}
\by R.~Sh.~Liptser, A.~N.~Shiryaev
\paper Nonlinear interpolation of components of diffusion Markov processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1968
\vol 13
\issue 4
\pages 602--620
\mathnet{http://mi.mathnet.ru/tvp896}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=240871}
\zmath{https://zbmath.org/?q=an:0177.45503|0174.49402}
\transl
\jour Theory Probab. Appl.
\yr 1968
\vol 13
\issue 4
\pages 564--583
\crossref{https://doi.org/10.1137/1113074}


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