Geodesic
Nonlinear interpolation of components of diffusion Markov processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 602-620 
R. Sh. Liptser; A. N. Shiryaev. Nonlinear interpolation of components of diffusion Markov processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 4, pp. 602-620. http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a1/
@article{TVP_1968_13_4_a1,
     author = {R. Sh. Liptser and A. N. Shiryaev},
     title = {Nonlinear interpolation of components of diffusion {Markov} processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {602--620},
     year = {1968},
     volume = {13},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_4_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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).