On the asymptotical normality of statistical solutions for harmonic crystals in half-space |
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Authors: | T V Dudnikova |
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Institution: | (1) Elektrostal Polytechnical Institute, Elektrostal, 144000, Russia |
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Abstract: | We consider the dynamics of a harmonic crystal in the half-space with zero boundary condition. It is assumed that the initial
date is a random function with zero-mean, finite-mean energy density which also satisfies a mixing condition of Rosenblatt
or Ibragimov type. We study the distribution μ
t
of the solution at time t ∈ ℝ. The main result is the convergence of μ
t
as t → ∞ to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian in
general).
Supported partly by research grant of RFBR (06-01-00096). |
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Keywords: | |
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