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Large deviations for random matricial moment problems

Author

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  • Gamboa, Fabrice
  • Nagel, Jan
  • Rouault, Alain
  • Wagener, Jens

Abstract

We consider the moment space MnK corresponding to p×p complex matrix measures defined on K (K=[0,1] or K=T). We endow this set with the uniform distribution. We are mainly interested in large deviation principles (LDPs) when n→∞. First we fix an integer k and study the vector of the first k components of a random element of MnK. We obtain an LDP in the set of k-arrays of p×p matrices. Then we lift a random element of MnK into a random measure and prove an LDP at the level of random measures. We end with an LDP on Carathéodory and Schur random functions. These last functions are well connected to the above random measure. In all these problems, we take advantage of the so-called canonical moments technique by introducing new (matricial) random variables that are independent and have explicit distributions.

Suggested Citation

  • Gamboa, Fabrice & Nagel, Jan & Rouault, Alain & Wagener, Jens, 2012. "Large deviations for random matricial moment problems," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 17-35.
    • Handle: RePEc:eee:jmvana:v:106:y:2012:i:c:p:17-35
    DOI: 10.1016/j.jmva.2011.11.006
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    Cited by:

    1. Dette, Holger & Tomecki, Dominik, 2019. "Determinants of block Hankel matrices for random matrix-valued measures," Stochastic Processes and their Applications, Elsevier, vol. 129(12), pages 5200-5235.
    2. Dette, Holger & Guhlich, Matthias & Nagel, Jan, 2014. "Distributions on matrix moment spaces," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 17-31.

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