Geodesic
A Functional Central Limit Theorem for Transformed Solutions of the Multidimensional Burgers Equation with Random Initial Data
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 3, pp. 427-448

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This paper states the convergence in distribution in some functional space to the Gaussian field with explicitly calculated parameters for transformed solutions of the multidimensional Burgers equation with initial conditions given by the associated random measure. Auxiliary moment and maximal inequalities obtained in the paper are of interest in themselves.
Keywords: nonlinear diffusion, associated random variables, moment inequalities, maximal inequalities. 
@article{TVP_2001_46_3_a1,
     author = {Yu. Yu. Bakhtin},
     title = {A {Functional} {Central} {Limit} {Theorem} for {Transformed} {Solutions} of the {Multidimensional} {Burgers} {Equation} with {Random} {Initial} {Data}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {427--448},
     publisher = {mathdoc},
     volume = {46},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a1/}
}
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Yu. Yu. Bakhtin. A Functional Central Limit Theorem for Transformed Solutions of the Multidimensional Burgers Equation with Random Initial Data. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 3, pp. 427-448. http://geodesic.mathdoc.fr/item/TVP_2001_46_3_a1/