Geodesic
On conditional distributions of diffusion processes
Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 336-356

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For a two-component diffusion process $(x,y)$ on the Euclidean space $R^n$ ($n\geqslant2$), we consider the question of the existence of the density $\pi_{t,s}$ of the distribution $P(x_t\in\nobreak\cdot\,|\,y_\tau,\ \tau\leqslant s)$, $s\leqslant t$, with respect to Lebesgue measure, and we study its analytic properties. We also consider the question of the existence and uniqueness of the solution of the equation for $\pi_{t,t}$ (the filtering equation). Bibliography: 18 titles. 
@article{IM2_1978_12_2_a8,
     author = {N. V. Krylov and B. L. Rozovskii},
     title = {On conditional distributions of diffusion processes},
     journal = {Izvestiya. Mathematics },
     pages = {336--356},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a8/}
}
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N. V. Krylov; B. L. Rozovskii. On conditional distributions of diffusion processes. Izvestiya. Mathematics , Tome 12 (1978) no. 2, pp. 336-356. http://geodesic.mathdoc.fr/item/IM2_1978_12_2_a8/