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Tail asymptotics for dependent subexponential differences. (English. Russian original) Zbl 1257.62016

Sib. Math. J. 53, No. 6, 965-983 (2012); translation from Sib. Mat. Zh. 53, No. 6, 1209-1230 (2012).
Summary: We study the asymptotic behavior of \(\mathbb P (X-Y>u)\) as \( u \to \infty\), where \(X\) is subexponential, \(Y\) is positive, and the random variables \(X\) and \(Y\) may be dependent. We give criteria under which the subtraction of \(Y\) does not change the tail behavior of \(X\). It is also studied under which conditions the comonotonic copula represents the worst-case scenario for the asymptotic behavior in the sense of minimizing the tail of \( X -Y\). Some explicit construction of the worst-case copula is provided in other cases.

MSC:

62E20 Asymptotic distribution theory in statistics
62G32 Statistics of extreme values; tail inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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References:

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