New duality theorems for marginal problems with some applications in stochastics. (English) Zbl 0746.60020

Levin, V. L.; Rachev, S. T.

Stability problems for stochastic models, Proc. 11th Int. Semin., Sukhumi/USSR 1987, Lect. Notes Math. 1412, 137-171 (1989).

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[For the entire collection see Zbl 0679.00014.]
In the first part the authors extend some duality theorems for marginal problems to the situation where additional moment type constraints are imposed. Some upper bounds are derived for the Kantorovich-Rubinstein distance in the case of the \(L_ 1\)-norm on \(\mathbb{R}^ m\). These improve upon some bounds of Zolotarev. Applications are given to normalized maxima, Rényi maxima and to an invariance principle for maxima.

Reviewer: L.Rüschendorf (Münster)

MSC:

60F05	Central limit and other weak theorems
62B10	Statistical aspects of information-theoretic topics
60F17	Functional limit theorems; invariance principles
46E27	Spaces of measures

Keywords:

limit theorem for maxima; duality theorems; marginal problems; Kantorovich-Rubinstein distance; invariance principle for maxima

Citations:

Zbl 0679.00014