Stochastic interpretation of quasilinear parabolic systems with cross-diffusion

Ya. I. Belopol'skaya

Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 2, pp. 268-299

Résumé

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.

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