Precise large deviations for sums of two-dimensional random vectors with dependent components of heavy tails

Xinmei Shen and Hailan Tian

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 21, 6357-6368

Abstract: This article focuses on the tail probabilities of the partial sums S→n=∑k=1nX→k$\vec{S}_{n}=\sum _{k=1}^{n}\vec{X}_{k}$ and the random sums S→N(t)=∑k=1N(t)X→k$\vec{S}_{N(t)}=\sum _{k=1}^{N(t)}\vec{X}_{k}$, where {X→k,k≥1}$\lbrace \vec{X}_{k}, k \ge 1\rbrace$ is a sequence of independent identically distributed non-negative random vectors with two dependent components (using copulas for operational risk measurement) having extended regularly varying tails, and N(t) is a counting process independent of the sequence {X→k,k≥1}$\lbrace \vec{X}_{k}, k \ge 1\rbrace$. Under some reasonable assumptions, some precise large deviation results for S→n$\vec{S}_{n}$ and S→N(t)$\vec{S}_{N(t)}$ are obtained in the componentwise way.

Date: 2016
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DOI: 10.1080/03610926.2013.839794

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