Geodesic
Stochastic interpretation of quasilinear parabolic systems with cross-diffusion
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 2, pp. 268-299

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We construct a stochastic interpretation of the generalized solution of the Cauchy problem for a strongly coupled system of quasilinear parabolic equations. To this end we derive a system of stochastic equations and prove that its solution allows us to construct a probabilistic representation of the original Cauchy problem solution and investigate its properties. Our construction of a probabilistic representation of the generalized solution of the Cauchy problem is crucially based on results of stochastic flow theory. 
@article{TVP_2016_61_2_a3,
     author = {Ya. I. Belopol'skaya},
     title = {Stochastic interpretation of quasilinear parabolic systems with cross-diffusion},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {268--299},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_2_a3/}
}
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Ya. I. Belopol'skaya. Stochastic interpretation of quasilinear parabolic systems with cross-diffusion. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 2, pp. 268-299. http://geodesic.mathdoc.fr/item/TVP_2016_61_2_a3/