Correction to: Weak and \(L^ p\)-invariance principles for sums of b- valued random variables. (English) Zbl 0604.60025

Philipp, Walter

Ann. Probab. 14, 1095-1101 (1986).

The proofs of the author’s theorems 1 and 2 in ibid. 8, 68-82 (1980; Zbl 0426.60033) in contain several gaps. They are corrected in the note. It is also remarked that the proof of theorem 4 of the same paper can be repaired only in the Gaussian case.

Reviewer: T.Inglot

MSC:

60F05	Central limit and other weak theorems
60F17	Functional limit theorems; invariance principles
60F25	\(L^p\)-limit theorems
60B10	Convergence of probability measures
60B12	Limit theorems for vector-valued random variables (infinite-dimensional case)

Keywords:

invariance principle; stable measure; Gaussian measure; domain of attraction

Citations:

Zbl 0426.60033