Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 725-737
Citer cet article
B. L. Rozovskiǐ. Filtering, smoothing and prediction of degenerate diffusion processes. Backward equations. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 725-737. http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a9/
@article{TVP_1983_28_4_a9,
author = {B. L. Rozovskiǐ},
title = {Filtering, smoothing and prediction of degenerate diffusion processes. {Backward} equations},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {725--737},
year = {1983},
volume = {28},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a9/}
}
TY - JOUR
AU - B. L. Rozovskiǐ
TI - Filtering, smoothing and prediction of degenerate diffusion processes. Backward equations
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1983
SP - 725
EP - 737
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a9/
LA - ru
ID - TVP_1983_28_4_a9
ER -
%0 Journal Article
%A B. L. Rozovskiǐ
%T Filtering, smoothing and prediction of degenerate diffusion processes. Backward equations
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1983
%P 725-737
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a9/
%G ru
%F TVP_1983_28_4_a9
Let $Z(t)=(X(t),Y(t))$ be a multidimensional degenerate Markov diffusion process and $f$ be a real function such that $\mathbf Mf^2(X(t))<\infty$. Equations for $$ \mathbf M_{z,3}[f(X(t))\mid Y(r),\,r\in[s,\tau]] $$ with respect to $z$, $s$($t$, $x$ are fixed) are presented. We apply these equations to the problem of backward smoothing of $X$.
