A variational formula on the Cramér function of series of independent random variables

A variational formula on the Cramér function of series of independent random variables

In (Zajkowski, Positivity 19:529–537, 2015 ) it has been proved some variational formula on the Legendre–Fenchel transform of the cumulant generating function (the Cramér function) of Rademacher series with coefficients in the space ℓ 1 . In this paper we show a generalization of this formula to ser...

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2017-03, Vol.21 (1), p.273-282
1. Verfasser: Zajkowski, Krzysztof
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Convex analysis
Econometrics
Fourier Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
Random variables
Statistics
Studies
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Zusammenfassung:In (Zajkowski, Positivity 19:529–537, 2015 ) it has been proved some variational formula on the Legendre–Fenchel transform of the cumulant generating function (the Cramér function) of Rademacher series with coefficients in the space ℓ 1 . In this paper we show a generalization of this formula to series of a larger class of any independent random variables with coefficients that belong to the space ℓ 2 .
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-016-0419-z