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Asymptotic properties of the algebraic moment range process

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Abstract

Let M n denote the n-th moment space of the set of all probability measures on the interval [0, 1], P n the uniform distribution on the set M n and r n + 1 the maximal range of the (n + 1)-th moments corresponding to a random moment point C n with distribution P n on M n . We study several asymptotic properties of the stochastic process (r ⌊nt⌋+1) t∈[0,T] if n → ∞. In particular weak convergence to a Gaussian process and a large deviation principle are established.

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Authors and Affiliations

  1. Mathematik III, NA 3 / 72, Universitätsstraße 150, 44780, Bochum, Germany

    H. Dette

  2. Laboratoire de Statistique et de Probabilités, UMR C5583, Université Paul Sabatier, 118 Route de Narbonne, 31062, Toulouse cedex 4, France

    F. Gamboa

Authors
  1. H. Dette
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  2. F. Gamboa
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Dette, H., Gamboa, F. Asymptotic properties of the algebraic moment range process. Acta Math Hung 116, 247–264 (2007). https://doi.org/10.1007/s10474-007-6047-0

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  • DOI: https://doi.org/10.1007/s10474-007-6047-0

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