On joint weak convergence of partial sum and maxima processes

2017/04/07 by Krizmanic, Danijel
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1704.02121

Abstract

For a strictly stationary sequence of random variables we derive functional convergence of the joint partial sum and partial maxima process under joint regular variation with index α∈ (0,2) and weak dependence conditions. The limiting process consists of an α--stable Lévy process and an extremal process. We also describe the dependence between these two components of the limit. The convergence takes place in the space of ℝ²--valued càdlàg functions on [0,1], with the Skorohod weak M₁ topology. We further show that this topology in general can not be replaced by the stronger (standard) M₁ topology.

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