This article is cited in 5 papers

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

E. S. Palamarchuk

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: 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.

Received: 19.05.2016
Revised: 07.05.2017

DOI: 10.4213/tvp5133

 English version: Theory of Probability and its Applications, 2018, 62:4, 522–533

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