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Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 4, Pages 654–669 (Mi tvp5133)  

This article is cited in 2 scientific papers (total in 2 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.

Funding Agency Grant Number
Russian Science Foundation 15-11-30042


DOI: https://doi.org/10.4213/tvp5133

Full text: PDF file (407 kB)
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English version:
Theory of Probability and its Applications, 2018, 62:4, 522–533

Bibliographic databases:

Received: 19.05.2016
Revised: 07.05.2017

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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  • http://mi.mathnet.ru/eng/tvp/v62/i4/p654

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. S. Palamarchuk, “O zadache optimalnogo upravleniya lineinoi stokhasticheskoi sistemoi s neogranichennoi na beskonechnosti neustoichivoi matritsei sostoyaniya”, Avtomat. i telemekh., 2019, no. 2, 64–80  mathnet  crossref  elib
    2. E. S. Palamarchuk, “O verkhnikh funktsiyakh dlya anomalnykh diffuzii, modeliruemykh protsessom Ornshteina–Ulenbeka s peremennymi koeffitsientami”, Teoriya veroyatn. i ee primen., 64:2 (2019), 258–282  mathnet  crossref  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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