Weak Convergence to Stochastic Integrals Driven by α-Stable Lévy Processes

2011/04/18 by Zhengyan Lin, Hanchao Wang, Lin, Zhengyan +1
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1104.3402

18pages

arxiv created 2014/11/15 · arxiv updated 2014/11/18

Abstract

We use the martingale convergence method to get the weak convergence theorem on general functionals of partial sums of independent heavy-tailed random variables. The limiting process is the stochastic integral driven by α-stable Lévy process. Our method is very powerful to obtain the limit behavior of heavy-tailed random variables.

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