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March 2015 Logarithmic asymptotics for multidimensional extremes under nonlinear scalings
K. M. Kosiński, M. Mandjes
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J. Appl. Probab. 52(1): 68-81 (March 2015). DOI: 10.1239/jap/1429282607

Abstract

Let W = {Wn: nN} be a sequence of random vectors in Rd, d ≥ 1. In this paper we consider the logarithmic asymptotics of the extremes of W, that is, for any vector q > 0 in Rd, we find that logP(there exists nN: Wn u q) as u → ∞. We follow the approach of the restricted large deviation principle introduced in Duffy (2003). That is, we assume that, for every q0, and some scalings {an}, {vn}, (1 / vn)logP(Wn / anu q) has a, continuous in q, limit JW(q). We allow the scalings {an} and {vn} to be regularly varying with a positive index. This approach is general enough to incorporate sequences W, such that the probability law of Wn / an satisfies the large deviation principle with continuous, not necessarily convex, rate functions. The equations for these asymptotics are in agreement with the literature.

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K. M. Kosiński. M. Mandjes. "Logarithmic asymptotics for multidimensional extremes under nonlinear scalings." J. Appl. Probab. 52 (1) 68 - 81, March 2015. https://doi.org/10.1239/jap/1429282607

Information

Published: March 2015
First available in Project Euclid: 17 April 2015

zbMATH: 1321.60048
MathSciNet: MR3336847
Digital Object Identifier: 10.1239/jap/1429282607

Subjects:
Primary: 60F10
Secondary: 60G70

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 1 • March 2015
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