The Entropic Erdős-Kac Limit Theorem

Bobkov, Sergey G.; Chistyakov, G. P.; Kösters, Holger

doi:10.1007/s10959-014-0550-3

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2019

2024

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Cited by 2 publications

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“…There is also an increasing interest to other limit theorems in other strong distances such as the relative Fisher information; cf. [11,12,44,45].…”

Section: Introductionmentioning

confidence: 99%

Rényi divergence and the central limit theorem

Bobkov¹,

Chistyakov²,

Götze³

2019

Ann. Probab.

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We explore properties of the χ 2 and more general Rényi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using these distances. Moreover, we derive exact rates of convergence in these distances with respect to an increasing number of summands.1991 Mathematics Subject Classification. Primary 60E.

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“…There is also an increasing interest to other limit theorems in other strong distances such as the relative Fisher information; cf. [11,12,44,45].…”

Section: Introductionmentioning

confidence: 99%

Rényi divergence and the central limit theorem

Bobkov¹,

Chistyakov²,

Götze³

2019

Ann. Probab.

Self Cite

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Non-uniform Bounds and Edgeworth Expansions in Self-normalized Limit Theorems

Beckedorf,

Rohde

2024

J Theor Probab

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We study Edgeworth expansions in limit theorems for self-normalized sums. Non-uniform bounds for expansions in the central limit theorem are established while imposing only minimal moment conditions. Within this result, we address the case of non-integer moments leading to a reduced remainder. Furthermore, we provide non-uniform bounds for expansions in local limit theorems. The enhanced tail accuracy of our non-uniform bounds allows for deriving an Edgeworth-type expansion in the entropic central limit theorem as well as a central limit theorem in total variation distance for self-normalized sums.

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The Entropic Erdős-Kac Limit Theorem

Abstract: We prove entropic and total variation versions of the Erdős-Kac limit theorem for the maximum of the partial sums of i.i.d. random variables with densities.2010 Mathematics Subject Classification. 60F05 (60E10, 94A15).

Cited by 2 publications

References 25 publications

Rényi divergence and the central limit theorem

Rényi divergence and the central limit theorem

Non-uniform Bounds and Edgeworth Expansions in Self-normalized Limit Theorems

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