Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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