Khasminskii's theorem for the Kolmogorov equation with partially degenerate diffusion matrix (Q6569617)

The authors study the stationary Kolmogorov equation with partially degenerate diffusion matrix and discontinuous drift coefficient.\N\NA nonnegative locally finite Borel measure \(\mu\) which is a solution of the Kolmogorov equation and for which \(\mu(\mathbb R^d)=1\) is called a probability solution. Conditions for the existence of a probability solution of the Kolmogorov equation are given by Khasminskii's theorem.\N\NThe authors provide new sufficient conditions for the existence of a probability solution. Examples demonstrating the application of these conditions are presented.