Geodesic
On Extrapolation of a Random Field Satisfying the Wave Equation
Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 2, pp. 220-223 
M. I. Fortus. On Extrapolation of a Random Field Satisfying the Wave Equation. Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 2, pp. 220-223. http://geodesic.mathdoc.fr/item/TVP_1963_8_2_a12/
@article{TVP_1963_8_2_a12,
     author = {M. I. Fortus},
     title = {On {Extrapolation} of a {Random} {Field} {Satisfying} the {Wave} {Equation}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {220--223},
     year = {1963},
     volume = {8},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1963_8_2_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper deals with the linear extrapolation problem for a random homogeneous field $u(t,x)$ satisfying the equation ${{\partial ^2 u}/{\partial t^2}}={{a^2\partial^2 u}/{\partial x^2}}$. Assuming that the field is known in the region $-c\leq x\leq c,t\leq -{c/a}$, best linear extrapolation formulas and mean square errors are given for any value $u(t,x)$ outside of this region.