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Displaying similar documents to “Ivo Vrkoč sexagenarian”

Asymptotic stability condition for stochastic Markovian systems of differential equations

Efraim Shmerling (2010)

Mathematica Bohemica

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Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by d X ( t ) = A ( ξ ( t ) ) X ( t ) d t + H ( ξ ( t ) ) X ( t ) d w ( t ) , where ξ ( t ) is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.