Abstract
In this paper we study the convergence of stochastic processes related to a random partial differential equation (PDE with random coefficients) of heat equation propagation type in a Kolmogorov's random velocity field. Then we are able to improve the results of Avellanda and Majda in the case of "shear-flow" advection-diffusion because we prove a convergence in law of the solution of the RPDE instead of just convergence of the moments.
Citation
Guillaume Gaudron. "Scaling laws and convergence for the advection-diffusion equation." Ann. Appl. Probab. 8 (3) 649 - 663, August 1998. https://doi.org/10.1214/aoap/1028903445
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