2019
Том 71
№ 11

All Issues

Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input

Lapshin A. L.

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Abstract

We derive equations that determine second moments of a random solution of a system of Itô linear differential equations with coefficients depending on a finite-valued random semi-Markov process. We obtain necessary and sufficient conditions for the asymptotic stability of solutions in the mean square with the use of moment equations and Lyapunov stochastic functions.

English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 6, pp 864-873.

Citation Example: Lapshin A. L. Equations for second moments of solutions of a system of linear differential equations with random semi-Markov coefficients and random input // Ukr. Mat. Zh. - 1999. - 51, № 6. - pp. 776–783.

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