Smooth invariant densities for random switching on the torus
Publication
, Journal Article
Bakhtin, Y; Hurth, T; Lawley, SD; Mattingly, JC
August 1, 2017
We consider a random dynamical system obtained by switching between the flows generated by two smooth vector fields on the 2d-torus, with the random switchings happening according to a Poisson process. Assuming that the driving vector fields are transversal to each other at all points of the torus and that each of them allows for a smooth invariant density and no periodic orbits, we prove that the switched system also has a smooth invariant density, for every switching rate. Our approach is based on an integration by parts formula inspired by techniques from Malliavin calculus.
Duke Scholars
Publication Date
August 1, 2017
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
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Bakhtin, Y., Hurth, T., Lawley, S. D., & Mattingly, J. C. (2017). Smooth invariant densities for random switching on the torus (Submitted).
Bakhtin, Y., T. Hurth, S. D. Lawley, and J. C. Mattingly. “Smooth invariant densities for random switching on the torus (Submitted),” August 1, 2017.
Bakhtin Y, Hurth T, Lawley SD, Mattingly JC. Smooth invariant densities for random switching on the torus (Submitted). 2017 Aug 1;
Bakhtin, Y., et al. Smooth invariant densities for random switching on the torus (Submitted). Aug. 2017.
Bakhtin Y, Hurth T, Lawley SD, Mattingly JC. Smooth invariant densities for random switching on the torus (Submitted). 2017 Aug 1;
Publication Date
August 1, 2017
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics