6533b855fe1ef96bd12b1380

RESEARCH PRODUCT

Characteristic Functions and the Central Limit Theorem

Achim Klenke

subject

Statistics::TheoryFactor theoremPure mathematicsArzelà–Ascoli theoremPicard–Lindelöf theoremMathematical analysisDanskin's theoremBrouwer fixed-point theoremSqueeze theoremMathematicsCarlson's theoremMean value theorem

description

The main goal of this chapter is the central limit theorem (CLT) for sums of independent random variables (Theorem 15.37) and for independent arrays of random variables (Lindeberg–Feller theorem, Theorem 15.43). For the latter, we prove only that one of the two implications (Lindeberg’s theorem) that is of interest in the applications.

yearjournalcountryeditionlanguage
2020-01-01
https://doi.org/10.1007/978-1-4471-5361-0_15