Linear systems with randomly interrupted Gaussian white noise

A linear process driven by additive Gaussian white noise, which is randomly interrupted by an exponentially correlated two-state (0,1) Markovian stochastic process, is considered. A characteristic function of the process is obtained using an approach based on conditional functionals for Markov processes. A single-event time dependent probability distribution is presented. Steady states are analysed in terms of stationary distributions and moments of the process. The deviation from Gaussianity (kurtosis) is investigated.

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