Exact Small Time Equivalent for the density of the Circular Langevin Diffusion

2015/10/14 by Jacques Franchi, Franchi, Jacques
Chemistry · Mathematics · Physics and Astronomy · #35K05 #60H07 #60J65 #Advanced NMR Techniques and Applications #FOS: Mathematics #Probability (math.PR) #Spectroscopy and Quantum Chemical Studies #math.PR #msc:35K05 #msc:35K65 #msc:58J65 #msc:60H07 #msc:60J65 #primary: 58J65 #secondary: 35K65 #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1510.04070

65 pages, 1 figure

arxiv created 2015/10/14 · openalex publication_date 2015/10/14 · arxiv updated 2015/10/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

A small time equivalent of the density is obtained for the circular analogue of the Langevin diffusion, which is strictly hypoelliptic (and non-Gaussian), hence of a different nature as the known sub-Riemannian case. The singular case, analogous to the case of conjugate points (the cut-locus problem) in the sub-Riemannian framework, is totally handled too, though much more difficultly.

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