Sidney Resnick

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We consider a simple stationary bilinear model Xt = cX t?1 Z t?1 + Zt; t = 0; 1;2; : : : generated by heavy tailed noise variables fZtg. A complete analysis of weak limit behavior is given by means of a point process analysis. A striking feature of this analysis is that the sample correlation converges in distribution to a non-degenerate limit. A warning is(More)
Huge data sets from the teletraac industry exhibit many non-standard characteristics such as heavy tails and long range dependence. Various estimation methods for heavy tailed time series with positive innovations are reviewed. These include parameterestimation and model identiicationmethods for autoregressionsand moving averages. Parameter estimation(More)
Cumulative broadband network traac is often thought to be well modelled by fractional Brownian motion. However, some traac measurements do not show an agreement with the Gaussian marginal distribution assumption. We show that if connection rates are modest relative to heavy tailed connection length distribution tails, then stable L evy motion is a sensible(More)
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation provides a rich description of extremal dependence in the case of asymptotic dependence, but fails to distinguish(More)
We discuss how long range dependence can innuence the characteristics of a single server queue. We take the analogue of the G/M/1 queue except that the input stream is altered to exhibit long range dependence. The equilibrium queue size and equilibrium waiting time distributions each have heavy tails. By suitably selecting the parameters of the inputs, the(More)