Analysis of the asymptotic behavior of the solution to a~linear stochastic differential equation with subexponentially stable matrix and its application to a~control problem
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 654-669
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We analyze the asymptotic behavior of the solution to a linear stochastic differential equation with subexponentially stable matrix. A result in the form of the strong law of large numbers is put forward for a pair of processes consisting of a squared norm of the solution and a deterministic function defined as an integral of the squared norm of the diffusion matrix. This result is applied in solving the problem of a linear-quadratic regulator over an infinite time-horizon for one class of undetectable systems.
Keywords:
strong law of large numbers, linear equation, nonexponential stability, linear-quadratic regulator.
@article{TVP_2017_62_4_a1,
author = {E. S. Palamarchuk},
title = {Analysis of the asymptotic behavior of the solution to a~linear stochastic differential equation with subexponentially stable matrix and its application to a~control problem},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {654--669},
publisher = {mathdoc},
volume = {62},
number = {4},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a1/}
}
TY - JOUR AU - E. S. Palamarchuk TI - Analysis of the asymptotic behavior of the solution to a~linear stochastic differential equation with subexponentially stable matrix and its application to a~control problem JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2017 SP - 654 EP - 669 VL - 62 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a1/ LA - ru ID - TVP_2017_62_4_a1 ER -
%0 Journal Article %A E. S. Palamarchuk %T Analysis of the asymptotic behavior of the solution to a~linear stochastic differential equation with subexponentially stable matrix and its application to a~control problem %J Teoriâ veroâtnostej i ee primeneniâ %D 2017 %P 654-669 %V 62 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a1/ %G ru %F TVP_2017_62_4_a1
E. S. Palamarchuk. Analysis of the asymptotic behavior of the solution to a~linear stochastic differential equation with subexponentially stable matrix and its application to a~control problem. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 4, pp. 654-669. http://geodesic.mathdoc.fr/item/TVP_2017_62_4_a1/