Very rare events for diffusion processes in short time
arXiv:1901.10025
Abstract
We study the large deviation estimates for the short time asymptotic behavior of a strongly degenerate diffusion process. Assuming a nilpotent structure of the Lie algebra generated by the driving vector fields, we obtain a graded large deviation principle and prove the existence of those "very rare events". In particular the first grade coincides with the classical Large Deviation Principle.
24 pages