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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 1, Pages 89–103 (Mi zvmmf9975)  

This article is cited in 7 scientific papers (total in 7 papers)

Asymptotic behavior of the solution to a linear stochastic differential equation and almost sure optimality for a controlled stochastic process

E. S. Palamarchuk

Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii pr. 47, Moscow, 117418, Russia

Abstract: The asymptotic behavior of a stochastic process satisfying a linear stochastic differential equation is analyzed. More specifically, the problem is solved of finding a normalizing function such that the normalized process tends to zero with probability 1. The explicit expression found for the function involves the parameters of the perturbing process, and the function itself has a simple interpretation. The solution of the indicated problem makes it possible to considerably improve almost sure optimality results for a stochastic linear regulator on an infinite time interval.

Key words: linear stochastic differential equation, almost sure convergence of stochastic processes, linear regulator, stochastic optimality, discounting, asymptotic solution method.

DOI: https://doi.org/10.7868/S0044466914010128

Full text: PDF file (472 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:1, 83–96

Bibliographic databases:

UDC: 519.63
Received: 13.03.2013

Citation: E. S. Palamarchuk, “Asymptotic behavior of the solution to a linear stochastic differential equation and almost sure optimality for a controlled stochastic process”, Zh. Vychisl. Mat. Mat. Fiz., 54:1 (2014), 89–103; Comput. Math. Math. Phys., 54:1 (2014), 83–96

Citation in format AMSBIB
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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, “Stabilization of linear stochastic systems with a discount: modeling and estimation of the long-term effects from the application of optimal control strategies”, Math. Models Comput. Simul., 7:4 (2015), 381–388  mathnet  crossref  mathscinet  elib
    2. E. S. Palamarchuk, “Stochastic optimality in the portfolio tracking problem involving investor's temporal preferences”, Autom. Remote Control, 78:8 (2017), 1523–1536  mathnet  crossref  elib
    3. E. S. Palamarchuk, “Analysis of criteria for long-run average in the problem of stochastic linear regulator”, Autom. Remote Control, 77:10 (2016), 1756–1767  mathnet  crossref  isi  elib
    4. E. Palamarchuk, “On infinite time linear-quadratic Gaussian control of inhomogeneous systems”, 2016 European Control Conference (ECC) (Aalborg, Denmark), IEEE, 2016, 2477–2482  crossref  isi
    5. 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”, Theory Probab. Appl., 62:4 (2018), 522–533  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. E. S. Palamarchuk, “On the generalization of logarithmic upper function for solution of a linear stochastic differential equation with a nonexponentially stable matrix”, Differ. Equ., 54:2 (2018), 193–200  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    7. E. S. Palamarchuk, “An analytic study of the Ornstein–Uhlenbeck process with time-varying coefficients in the modeling of anomalous diffusions”, Autom. Remote Control, 79:2 (2018), 289–299  mathnet  crossref  mathscinet  zmath  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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