Convergence to Stable Laws in Relative Entropy
S.G. Bobkov, G. P. Chistyakov, F. G\"otze
TL;DR
This paper proves that the sum of i.i.d. random variables converges to a stable law when measured using relative entropy, extending classical limit theorems to an information-theoretic context.
Contribution
It introduces a new framework for analyzing convergence to stable laws via relative entropy, which was not previously established.
Findings
Convergence in relative entropy to stable laws is proven for i.i.d. sums.
The results extend classical limit theorems to an information-theoretic setting.
Provides conditions under which convergence in relative entropy occurs.
Abstract
Convergence to stable laws in relative entropy is established for sums of i.i.d. random variables.
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Taxonomy
TopicsWireless Communication Security Techniques · Statistical Mechanics and Entropy · Computability, Logic, AI Algorithms