The Stokes phenomenon for some moment partial differential equations

We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex plane but finitely many singular or branching points with the appropriate growth condition at the infinity. The main tools are the theory of summability and multisummability, and the theory of hyperfunctions. Using them we describe Stokes lines, anti-Stokes lines, jumps across Stokes lines, and a maximal family of solutions.