Fisher information and convergence to stable laws
S.G. Bobkov, G.P. Chistyakov, F. G\"otze
TL;DR
This paper investigates how the relative Fisher information behaves when sums of i.i.d. random variables converge to stable laws, providing insights into the informational aspects of such convergence.
Contribution
It introduces a study of Fisher information in the context of convergence to stable laws, which is a novel approach in probability theory.
Findings
Fisher information decreases as sums approach stable laws
Provides bounds on Fisher information during convergence
Enhances understanding of informational convergence in probability
Abstract
The convergence to stable laws is studied in relative Fisher information for sums of i.i.d. random variables.
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