Probabilistic approximation of the solution of the Cauchy problem for the higher-order Schrödinger equation

We propose two methods of approximation of the solution of the Cauchy problem for the higher-order Schrödinger equation. In the first method, the expectation of a functional of some random point field is used, and in the second, the expectation of a functional of the normed sums of independent and identically distributed random variables with finite moment of order $2m+2$ is employed.