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Energy estimate for the wave equation driven by a fractional Gaussian noise

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  • We consider a general linear stochastic wave equation driven by fractional-in-time noise and study its energy. We provide a mild solution for the wave equation in terms its Fourier expansion. We calculate the expected energy and give asymptotic results for the expected energy for large and small times and as the Hurst parameter, H, approaches 1/2. These results are phrased in terms of the norms of powers of the differential operator times powers of the spatial covariance operator.
    Mathematics Subject Classification: Primary: 60H15; Secondary: 35R60.


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