Abstract
In this paper given a macroscopic model of a phenomenon presented in terms of a system of fully coupled nonlinear parabolic equations we construct a correspondent microscopic model presented in terms of a system of stochastic equations with coefficients depending on their distributions. From mathematical point of view it leads to a construction of a probabilistic representation for a distributional solution of the Cauchy problem for the parabolic system with nondiagonal principal part. A crucial role in our construction is played by Kunita’s theory of stochastic flows which allows to construct a probabilistic representation for a distributional solution of the Cauchy problem for a single parabolic equation.
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Financial support of grant RFBR 12-01-00427-a and the Minobrnauki project N 2074 are gratefully acknowledged.
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Belopolskaya, Y. (2014). Probabilistic Counterparts for Strongly Coupled Parabolic Systems. In: Melas, V., Mignani, S., Monari, P., Salmaso, L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2104-1_5
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DOI: https://doi.org/10.1007/978-1-4939-2104-1_5
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