Geodesic
Problem of reconstructing a disturbance in a linear stochastic equation: the case of incomplete information
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 214-221

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of reconstructing an unknown deterministic disturbance characterizing the level of random noise in a linear stochastic second-order equation is investigated based on the approach of dynamic inversion theory. The reconstruction is performed with the use of discrete information on a number of realizations of one coordinate of the stochastic process. The problem under consideration is reduced to an inverse problem for a system of ordinary differential equations describing the covariance matrix of the original process. A finite-step solving algorithm based on the method of auxiliary controlled models is suggested. Its convergence rate estimate with respect to the number of measured realizations is obtained.
Keywords: reconstruction of disturbance, stochastic differential equation, incomplete input information. 
@article{TIMM_2013_19_4_a21,
     author = {V. L. Rozenberg},
     title = {Problem of reconstructing a disturbance in a linear stochastic equation: the case of incomplete information},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {214--221},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a21/}
}
TY  - JOUR
AU  - V. L. Rozenberg
TI  - Problem of reconstructing a disturbance in a linear stochastic equation: the case of incomplete information
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2013
SP  - 214
EP  - 221
VL  - 19
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a21/
LA  - ru
ID  - TIMM_2013_19_4_a21
ER  - 
%0 Journal Article
%A V. L. Rozenberg
%T Problem of reconstructing a disturbance in a linear stochastic equation: the case of incomplete information
%J Trudy Instituta matematiki i mehaniki
%D 2013
%P 214-221
%V 19
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a21/
%G ru
%F TIMM_2013_19_4_a21
V. L. Rozenberg. Problem of reconstructing a disturbance in a linear stochastic equation: the case of incomplete information. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 214-221. http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a21/