Invariant densities for dynamical systems with random switching
  We consider a non-autonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we show that H\"ormander type hypoellipticity conditions are sufficient for uniqueness and absolute continuity of an invariant measure. 
Yuri Bakhtin and Tobias Hurth
math.DS math.PR