Weak Convergence to Stochastic Integrals Driven by $\alpha-$Stable L\'evy Processes

Zhengyan Lin; Hanchao Wang

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arXiv · 1104.3402

Weak Convergence to Stochastic Integrals Driven by $\alpha-$Stable L\'evy Processes

Zhengyan Lin·Hanchao Wang

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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 $\alpha-$stable L\'evy process. Our method is very powerful to obtain the limit behavior of heavy-tailed random variables.

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Zhengyan Lin, Hanchao Wang. 2011-04-18. Weak Convergence to Stochastic Integrals Driven by $\alpha-$Stable L\'evy Processes. https://arxiv.org/abs/1104.3402

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