Invariant densities for dynamical systems with random switching

Abstract

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 Hörmander type hypoellipticity conditions are sufficient for uniqueness and absolute continuity of an invariant measure.

16 pages; we replaced our original article to point out and close a gap in the discussion of the Lorenz system in Section 7 (see Remark 2); this gap is only present in the journal version of this article --- it wasn't present in the previous arxiv version

References in corpus (1)

• On finite-dimensional projections of distributions for solutions of randomly forced PDE's

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