On overload in a storage model, with a self-similar and infinitely divisible input

Details On overload in a storage model, with a self-similar and infinitely divisible input On overload in a storage model, with a self-similar and infinitely divisible input

2004-05-14

arxiv.org/abs/math/0405291v1

Annals of Applied Probability 2004, Vol. 14, No. 2, 820-844

Mathematics

Probability

Scientific paper

10.1214/105051604000000125

Let {X(t)}_{t\ge0} be a locally bounded and infinitely divisible stochastic process, with no Gaussian component, that is self-similar with index H>0. Pick constants \gamma >H and c>0. Let \nu be the L\'evy measure on R^{[0,\infty)} of X, and suppose that R(u)\equiv\nu({y\inR^{[0,\infty)}:supt\ge 0y(t)/(1+ct^{\gamma})>u}) is suitably ``heavy tailed'' as u\to\infty (e.g., subexponential with positive decrease). For the ``storage process'' Y(t)\equiv sup_{s\ge t}(X(s)-X(t)-c(s-t)^{\gamma}), we show that P{sup_{s\in[0,t(u)]}Y(s)>u}\sim P{Y(\hat t(u))>u} as u\to\infty, when 0\le \hat t(u)\le t(u) do not grow too fast with u [e.g., t(u)=o(u^{1/\gamma})].

Affiliated with

Also associated with

No associations

Rating

On overload in a storage model, with a self-similar and infinitely divisible input does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On overload in a storage model, with a self-similar and infinitely divisible input, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On overload in a storage model, with a self-similar and infinitely divisible input will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-671781