Open Access
2017 Duality and hypoellipticity: one-dimensional case studies
Laurent Miclo
Electron. J. Probab. 22: 1-32 (2017). DOI: 10.1214/17-EJP114


To visualize how the randomness of a Markov process $X$ is spreading, one can consider subset-valued dual processes $I$ constructed by intertwining. In the framework of one-dimensional diffusions, we investigate the behavior of such dual processes $I$ in the presence of hypoellipticity for $X$. The Pitman type property asserting that the measure of $I$ is a time-changed Bessel 3 process is preserved, the effect of hypoellipticity is only found at the level of the time change. It enables to recover the density theorem of Hörmander in this simple degenerate setting, as well as to construct strong stationary times by introducing different dual processes.


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Laurent Miclo. "Duality and hypoellipticity: one-dimensional case studies." Electron. J. Probab. 22 1 - 32, 2017.


Received: 6 April 2017; Accepted: 2 October 2017; Published: 2017
First available in Project Euclid: 20 October 2017

zbMATH: 06797901
MathSciNet: MR3718719
Digital Object Identifier: 10.1214/17-EJP114

Primary: 60J60
Secondary: 35K65 , 37A25 , 60F05 , 60H30 , 60J35

Keywords: Bessel 3 process , duality by intertwining , Hörmander’s density theorem , Hypoellipticity , one-dimensional diffusions , strong stationary times

Vol.22 • 2017
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