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Choi, Byoung Jin; Ji, Un Cig

Exponential convergence rates for weighted sums in noncommutative probability space. (English) Zbl 1370.46040

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19, No. 4, Article ID 1650027, 13 p. (2016).
Weighted sums of independent random variables (with a triangular array of coefficients) in tracial \(W^*\)-probability spaces are investigated. The mainly used notion of noncommutative independence is called strong independence: this is factorization of the trace for disjoint index sets of the variables. For some results, successive independence is enough.
Conditions for exponential convergence of such weighted sums are provided, which generalize the classical results in [L. E. Baum et al., Trans. Am. Math. Soc. 102, 187–199 (1962; Zbl 0107.13201)]. Applications are given to large deviations and to free additive convolutions of probability measures.
Reviewer: Rolf Gohm (Aberystwyth)

Cited in 5 Documents

MSC:

46L53 Noncommutative probability and statistics

Keywords:

noncommutative probability space; free convolutionability space; weighted sum; weak law of large numbers; exponential convergence rate; large deviation principle; free convolution

Citations:

Zbl 0107.13201
PDFBibTeX XMLCite
\textit{B. J. Choi} and \textit{U. C. Ji}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19, No. 4, Article ID 1650027, 13 p. (2016; Zbl 1370.46040)
Full Text: DOI

References:

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