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Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by $\mathrm{d}X\left(t\right)=A\left(\xi \right(t\left)\right)X\left(t\right)\mathrm{d}t+H\left(\xi \right(t\left)\right)X\left(t\right)\mathrm{d}w\left(t\right)$, where $\xi \left(t\right)$ 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.