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On the Generalization of Logarithmic Upper Function for Solution of a Linear Stochastic Differential Equation with a Nonexponentially Stable Matrix

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Abstract

The problem of finding the upper function for the squared norm of the solution of a linear stochastic differential equation with a nonexponentially stable matrix is solved. A novel characteristic of a nonconstant stability rate of the matrix is introduced. The determined upper function generalizes the previously known logarithmic estimate and is expressed in closed form in terms of the rate of matrix stability. Examples of determining the upper function for different stability rates are provided.

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Authors and Affiliations

  1. Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, 117418, Russia

    E. S. Palamarchuk

  2. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991, Russia

    E. S. Palamarchuk

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  1. E. S. Palamarchuk
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Correspondence to E. S. Palamarchuk.

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Original Russian Text © E.S. Palamarchuk, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 2, pp. 195–201.

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Palamarchuk, E.S. On the Generalization of Logarithmic Upper Function for Solution of a Linear Stochastic Differential Equation with a Nonexponentially Stable Matrix. Diff Equat 54, 193–200 (2018). https://doi.org/10.1134/S0012266118020064

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  • DOI: https://doi.org/10.1134/S0012266118020064

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