Completeness property for plans of sequential estimation for Wiener processes with a~drift and some uniqueness theorems
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XII, Tome 126 (1983), pp. 69-72
Voir la notice de l'article provenant de la source Math-Net.Ru
The family of $n$-dimensional Wiener processes $x_\lambda(t)=\xi(t)+\lambda t$ is consedered, $\xi(t)$ being the standard Wiener process. Let $\Gamma$ be a “plan”, defined by some closed subset $\Gamma\subset\mathbb R^n\times\mathbb R_+$ and let $\mu_\lambda$ be the corresponding probability measure on $\Gamma$ defined by the first entrance into $\Gamma$. Conditions are given for the plans to posess the completeness property, i. e. for the implication $\int_\Gamma f(x)\,\mu_\lambda(dx)=0\;\forall\lambda\Rightarrow f\equiv0$ to hold.
@article{ZNSL_1983_126_a7,
author = {V. P. Gurarii and V. I. Matsaev},
title = {Completeness property for plans of sequential estimation for {Wiener} processes with a~drift and some uniqueness theorems},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {69--72},
publisher = {mathdoc},
volume = {126},
year = {1983},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a7/}
}
TY - JOUR AU - V. P. Gurarii AU - V. I. Matsaev TI - Completeness property for plans of sequential estimation for Wiener processes with a~drift and some uniqueness theorems JO - Zapiski Nauchnykh Seminarov POMI PY - 1983 SP - 69 EP - 72 VL - 126 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a7/ LA - ru ID - ZNSL_1983_126_a7 ER -
%0 Journal Article %A V. P. Gurarii %A V. I. Matsaev %T Completeness property for plans of sequential estimation for Wiener processes with a~drift and some uniqueness theorems %J Zapiski Nauchnykh Seminarov POMI %D 1983 %P 69-72 %V 126 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a7/ %G ru %F ZNSL_1983_126_a7
V. P. Gurarii; V. I. Matsaev. Completeness property for plans of sequential estimation for Wiener processes with a~drift and some uniqueness theorems. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XII, Tome 126 (1983), pp. 69-72. http://geodesic.mathdoc.fr/item/ZNSL_1983_126_a7/