Fisher information bounds and applications to SDEs with small noise

Nguyen Tien Dung; Nguyen Thu Hang

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arXiv · 2408.09797

Fisher information bounds and applications to SDEs with small noise

Nguyen Tien Dung·Nguyen Thu Hang

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Abstract

In this paper, we first establish general bounds on the Fisher information distance to the class of normal distributions of Malliavin differentiable random variables. We then study the rate of Fisher information convergence in the central limit theorem for the solution of small noise stochastic differential equations and its additive functionals. We also show that the convergence rate is of optimal order.

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Nguyen Tien Dung, Nguyen Thu Hang. 2024-08-19. Fisher information bounds and applications to SDEs with small noise. https://arxiv.org/abs/2408.09797

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