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Teor. Veroyatnost. i Primenen., 1981, Volume 26, Issue 4, Pages 734–744 (Mi tvp3503)  

Quadratic Lyapunov's functionals and the second moments for stochastic systems with an after-effect

G. N. Mil'šteĭn

Sverdlovsk

Abstract: We introduce two positive semigroups of class $C_0$ in a locally convex space of self-adjoint bounded operators defined on a Hilbert space. This semigroups are connected with the quadratic functionals and second moments for stochastic systems with an after-effect. The formulas for the infinitesimal operators of this semigroups are obtained. Our results permit us to formulate the criterions for the mean square stability within the framework of the second Lyapunov's method.

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English version:
Theory of Probability and its Applications, 1982, 26:4, 721–731

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Received: 18.01.1979

Citation: G. N. Mil'šteǐn, “Quadratic Lyapunov's functionals and the second moments for stochastic systems with an after-effect”, Teor. Veroyatnost. i Primenen., 26:4 (1981), 734–744; Theory Probab. Appl., 26:4 (1982), 721–731

Citation in format AMSBIB
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\by G.~N.~Mil'{\v s}te{\v\i}n
\paper Quadratic Lyapunov's functionals and the second moments for stochastic systems with an after-effect
\jour Teor. Veroyatnost. i Primenen.
\yr 1981
\vol 26
\issue 4
\pages 734--744
\mathnet{http://mi.mathnet.ru/tvp3503}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=636768}
\zmath{https://zbmath.org/?q=an:0486.93058}
\transl
\jour Theory Probab. Appl.
\yr 1982
\vol 26
\issue 4
\pages 721--731
\crossref{https://doi.org/10.1137/1126079}
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