Regularity of invariant densities for 1D systems with random switching

This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.

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Bibliographic Details
Published in:Nonlinearity 2015-10, Vol.28 (11), p.3755-3787
Main Authors: Bakhtin, Yuri, Hurth, Tobias, Mattingly, Jonathan C
Format: Article
Language:English
Subjects:
invariant densities
piecewise deterministic Markov processes
randomly switched ODEs
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Description
Summary:This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove the smoothness of the invariant densities away from critical points and describe the asymptotics of the invariant densities at critical points.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/28/11/3755