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This work is devoted to almost sure and moment exponential stability of regimeswitching jump diffusions. The Lyapunov function method is used to derive sufficient conditions for stabilities for general nonlinear systems; which further helps to derive easily verifiable conditions for linear systems. For one-dimensional linear regime-switching jump diffusions, necessary and sufficient conditions for almost sure and pth moment exponential stabilities are presented. Several examples are provided for illustration.

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