Parabolic Behavior of a Hyperbolic Delay Equation

@article{Laurent2006ParabolicBO,
  title={Parabolic Behavior of a Hyperbolic Delay Equation},
  author={Thomas Laurent and Brian Rider and Michael C. Reed},
  journal={SIAM J. Math. Anal.},
  year={2006},
  volume={38},
  pages={1-15}
}
It is shown that the fundamental solution of a hyperbolic partial differential equation with time delay has a natural probabilistic structure, i.e., is approximately Gaussian, as $t \rightarrow \infty.$ The proof uses ideas from the DeMoivre proof of the central limit theorem. It follows that solutions of the hyperbolic equation look approximately like solutions of a diffusion equation with constant convection as $t \rightarrow \infty.$ 

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