Abstract
We study the scaling limit of random fields which are the solutions of a nonlinear partial differential equation known as the Burgers equation, under stochastic initial condition. These are assumed to be a Gaussian process with long-range dependence. We present some results on the rate of convergence to the normal law.
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Leonenko, N.N., Orsingher, E. & Parkhomenko, V.N. On the rate of convergence to the normal law for solutions of the Burgers equation with singular initial data. J Stat Phys 82, 915–930 (1996). https://doi.org/10.1007/BF02179795
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DOI: https://doi.org/10.1007/BF02179795