Theory of Probability and Mathematical Statistics
Non-central limit theorem for the spatial average of the solution to the wave equation with Rosenblatt noise
R. Dhoyer and C. A. Tudor
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Abstract: We analyze the limit behavior in distribution of the spatial average of the solution to the wave equation driven by the two-parameter Rosenblatt process in spatial dimension d=1. We prove that this spatial average satisfies a non-central limit theorem, more precisely it converges in law to a Wiener integral with respect to the Rosenblatt process. We also give a functional version of this limit theorem.
Keywords: Stochastic wave equation, Rosenblatt sheet, cumulants, multiple stochastic integrals, second Wiener chaos
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