Geodesic
Estimation of the mean of a Wiener process observed on an infinite interval
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 804-808

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Let $\omega(t)$ be a Wiener process, $\mathbf{M}\omega(t)=0$, $\mathbf{D}\omega(t)=t$, $\varphi(t)$, $t\in[0,\infty]$ be a function form a set $M\subset C_{[0,\infty)}$ and $x(t)=\omega(t)+\varphi(t)$ be the observation process. In the paper, conditions on the set $M$ are given under which there exist a consistent estimate of $\varphi$. 
@article{TVP_1973_18_4_a8,
     author = {I. Sh. Ibramhalilov and A. V. Skorokhod},
     title = {Estimation of the mean of a {Wiener} process observed on an infinite interval},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {804--808},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a8/}
}
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I. Sh. Ibramhalilov; A. V. Skorokhod. Estimation of the mean of a Wiener process observed on an infinite interval. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 4, pp. 804-808. http://geodesic.mathdoc.fr/item/TVP_1973_18_4_a8/