A decomposition-homogenization method for Robin boundary problems on the nonnegative orthant

This paper studies the existence and uniqueness of a classical solution to a type of Robin boundary problems on the nonnegative orthant. We propose a new decomposition-homogenization method for the Robin boundary problem based on probabilistic rep-resentations, which leads to two auxiliary Robin boundary problems admitting some simplified probabilistic representations. The auxiliary probabilistic representations allow us to establish the existence of a unique classical solution to the original Robin boundary problem using some stochastic flow analysis.