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The Classical Central Limit Theorem
- Source :
- Stochastic Limit Theory ISBN: 0192844504, Stochastic Limit Theory
- Publication Year :
- 2021
- Publisher :
- Oxford University PressOxford, 2021.
-
Abstract
- In this chapter, the first approach is made to establishing the convergence of scaled random sums, considering independent sequences. The classic Lindeberg–Lévy, Khinchine, Lindeberg–Feller, and Liapunov theorems are proved. The main focus is on the treatment of heterogeneous summands, applying the Lindeberg condition, and extensions are given to allow trending (growing or shrinking) variances. The final sections review cases of the central limit theorem under non-standard conditions and α-stable convergence.
Details
- ISBN :
- 978-0-19-284450-7
0-19-284450-4 - ISBNs :
- 9780192844507 and 0192844504
- Database :
- OpenAIRE
- Journal :
- Stochastic Limit Theory ISBN: 0192844504, Stochastic Limit Theory
- Accession number :
- edsair.doi.dedup.....1ca07556dfc4efa1fc1b7d5ad043878a