3:10-3:50 Sidney Resnick, Cornell University Title: Asymptotic Methods for Extremal Dependence

Abstract: Measuring asymptotic dependence between components of a vector or stochastic process using asymptotic methods is a slippery slope. One asymptotic regime may indicate components are "asymptotically independent" but on a different scale, that is, using a different asymptotic regime, the components may be asymptotically dependent. We present a framework for mathematically formulating asymptotic approximations for the probability of remote risk regions and give some examples where an infinite sequence of asymptotic regimes exist. The examples apply to regularly varying sequences and L\'evy processes whose L\'evy measure is regularly varying.

Workshop on Measures of Extremal DependenceMay 3rd, 20133:10-3:50 Sidney Resnick, Cornell UniversityTitle: Asymptotic Methods for Extremal Dependence

Abstract:Measuring asymptotic dependence between components of a vector or stochastic process using asymptotic methods is a slippery slope. One asymptotic regime may indicate components are "asymptotically independent" but on a different scale, that is, using a different asymptotic regime, the components may be asymptotically dependent. We present a framework for mathematically formulating asymptotic approximations for the probability of remote risk regions and give some examples where an infinite sequence of asymptotic regimes exist. The examples apply to regularly varying sequences and L\'evy processes whose L\'evy measure is regularly varying.