Hölder regularity of stationary measures

Anton Gorodetski, Victor Kleptsyn, Grigorii Monakov

Published 2022-09-25Version 1

We consider smooth random dynamical systems defined by a distribution with a finite moment of the norm of the differential, and prove that under suitable non-degeneracy conditions any stationary measure must be H\"older continuous. The result is a vast generalization of the classical statement on H\"older continuity of stationary measures of random walks on linear groups.