Estimates for the distances between solutions to Kolmogorov equations with diffusion matrices of low regularity

Vladimir I. Bogachev; Stanislav V. Shaposhnikov

Paper

Estimates for the distances between solutions to Kolmogorov equations with diffusion matrices of low regularity

Abstract

We obtain estimates for the weighted

-norm of the difference of two probability solutions to Kolmogorov equations in terms of the difference of the diffusion matrices and the drifts. Unlike the previously known results, our estimate does not involve Sobolev derivatives of solutions and coefficients. The diffusion matrices are supposed to be non-singular, bounded and satisfy the Dini mean oscillation condition.