Stochastic models for fully coupled systems of nonlinear parabolic equations

Yana Belopolskaya

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arXiv · 1705.01119

Stochastic models for fully coupled systems of nonlinear parabolic equations

Yana Belopolskaya

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Abstract

We construct a probabilistic representation of a system of fully coupled parabolic equations arising as a model describing spatial segregation of interacting population species. We derive a closed system of stochastic equations such that its solution allows to obtain a probabilistic representation of a weak solution of the Cauchy problem for the PDE system. The corresponded stochastic system is presented in the form of a system of stochastic equations describing nonlinear Markov processes and their multiplicative functionals.

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Yana Belopolskaya. 2017-05-02. Stochastic models for fully coupled systems of nonlinear parabolic equations. https://arxiv.org/abs/1705.01119

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