Lena Jonas
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Lena Jonas has a total of 1 co-authors. Here are the top co-authors by number of shared publications:
- Lutz Mattner
Universität Trier, Fachbereich IV – Mathematik, 54286 Trier, Germany
1 shared publication
Latest Publications
- 17 November 2025
- Published by American Mathematical Society (AMS) in Theory of Probability and Mathematical Statistics
- Vol. 113, 113-132
A sharper Lyapunov–Katz central limit error bound for i.i.d. summands Zolotarev-close to normal
We prove a central limit error bound for convolution powers of laws with finite moments of order r ∈ ] 2 , 3 ] r \in ]2,3] , taking a closeness of the laws to normality into account. Up to a universal constant, this generalises the case of r = 3 r=3 of the sharpening of the Berry (1941) – Esseen (1942) theorem obtained by Mattner (2024), namely by sharpening here the Katz (1963) error bound for the i.i.d. case of Lyapunov’s (1901) theorem. Our proof uses a partial generalisation of the theorem of Senatov and Zolotarev (1986) used for the earlier special case. A result more general than our main one could be obtained by using instead another theorem of Senatov (1980), but, unfortunately, an auxiliary inequality used in the latter’s proof is wrong.
- 17 November 2025
- Published by American Mathematical Society (AMS) in Theory of Probability and Mathematical Statistics
- Vol. 113, 113-132
A sharper Lyapunov–Katz central limit error bound for i.i.d. summands Zolotarev-close to normal
We prove a central limit error bound for convolution powers of laws with finite moments of order r ∈ ] 2 , 3 ] r \in ]2,3] , taking a closeness of the laws to normality into account. Up to a universal constant, this generalises the case of r = 3 r=3 of the sharpening of the Berry (1941) – Esseen (1942) theorem obtained by Mattner (2024), namely by sharpening here the Katz (1963) error bound for the i.i.d. case of Lyapunov’s (1901) theorem. Our proof uses a partial generalisation of the theorem of Senatov and Zolotarev (1986) used for the earlier special case. A result more general than our main one could be obtained by using instead another theorem of Senatov (1980), but, unfortunately, an auxiliary inequality used in the latter’s proof is wrong.