Very rare events for diffusion processes in short time

Gérard Ben Arous; Jing Wang

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arXiv · 1901.10025

Very rare events for diffusion processes in short time

Gérard Ben Arous·Jing Wang

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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.

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Gérard Ben Arous, Jing Wang. 2019-01-28. Very rare events for diffusion processes in short time. https://arxiv.org/abs/1901.10025

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