On Overload in a Storage Model , with a Self-similar and Infinitely Divisible Input

@inproceedings{Albin2004OnOI,
  title={On Overload in a Storage Model , with a Self-similar and Infinitely Divisible Input},
  author={By J. M. P. Albin and Gennady Samorodnitsky},
  year={2004}
}
Let {X(t)}t≥0 be a locally bounded and infinitely divisible stochastic process, with no Gaussian component, that is self-similar with index H > 0. Pick constants γ > H and c > 0. Let ν be the Lévy measure on R of X, and suppose that R(u)≡ ν({y ∈ R : supt≥0 y(t)/(1 + ct ) > u}) is suitably “heavy tailed” as u →∞ (e.g., subexponential with positive decrease). For the “storage process” Y (t) ≡ sups≥t(X(s)−X(t)− c(s − t)), we show that P{sups∈[0,t(u)] Y (s) > u} ∼P{Y (t̂(u)) > u} as u →∞, when 0≤ t… CONTINUE READING