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Teoriya Veroyatnostei i ee Primeneniya, 2017, Volume 62, Issue 4, Pages 654–669
DOI: https://doi.org/10.4213/tvp5133 (Mi tvp5133) 		 
This article is cited in 5 scientific papers (total 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
Full-text PDF (407 kB) Citations (5)
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DOI: https://doi.org/10.4213/tvp5133
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.
Funding agency Grant number
Russian Science Foundation 15-11-30042
This work was supported by the Russian Science Foundation at the Steklov Mathematical Institute of Russian Academy of Sciences (grant 15-11-30042).
Received: 19.05.2016
Revised: 07.05.2017
English version:
Theory of Probability and its Applications, 2018, Volume 62, Issue 4, Pages 522–533
DOI: https://doi.org/10.1137/S0040585X97T988794
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: 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”, Teor. Veroyatnost. i Primenen., 62:4 (2017), 654–669; Theory Probab. Appl., 62:4 (2018), 522–533
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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