1,637 research outputs found
Tail asymptotics for dependent subexponential differences
We study the asymptotic behavior of ℙ(X − Y > u) as u → ∞, 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 case
Tail asymptotics for dependent subexponential differences
We study the asymptotic behavior of ℙ(X − Y > u) as u → ∞, 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
On the infimum attained by a reflected L\'evy process
This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected
at 0), and focuses on the distribution of , that is, the minimal value
attained in an interval of length (where it is assumed that the queue is in
stationarity at the beginning of the interval). The first contribution is an
explicit characterization of this distribution, in terms of Laplace transforms,
for spectrally one-sided L\'evy processes (i.e., either only positive jumps or
only negative jumps). The second contribution concerns the asymptotics of
\prob{M(T_u)> u} (for different classes of functions and large);
here we have to distinguish between heavy-tailed and light-tailed scenarios
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