Stochastic model of the Cauchy–Robin problem for systems of nonlinear parabolic equations

We derive stochastic equations to describe reflected diffusion processes associated with the Cauchy–Neumann problem for systems of nonlinear parabolic equations in non-divergent form. The construction of a solution to the arized stochastic problem is based on a localization procedure that allows to reduce the problem in a closed domain to the corresponding problem in the half space. As a result we obtain a probabilistic representation of a weak solution to the Cauchy–Neumann problem in a bounded domain with a smooth boundary.