Theory of Probability and Mathematical Statistics
Some vector-valued examples of noncentral moderate deviation results
Claudio Macci and Barbara Pacchiarotti
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Abstract: The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probability to a constant (governed by a reference large deviation principle) and a weak convergence to a non-Gaussian (and non-degenerating) distribution. Several examples can be found in the literature, mainly for real-valued random variables. In this paper, we present some examples with vector-valued random variables.
Keywords: Lévy processes, inverse stable subordinator, compound Poisson distribution, logistic normal distribution, skew normal distributions
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