A functional limit theorem for self-normalized partial sum processes in the $M_{1}$ topology

Danijel Krizmanic

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arXiv · 2411.18236

A functional limit theorem for self-normalized partial sum processes in the $M_{1}$ topology

Danijel Krizmanic

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Abstract

For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The convergence takes place in the space of real-valued cadlag functions on $[0,1]$ with the Skorokhod $M_{1}$ topology.

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Danijel Krizmanic. 2024-11-27. A functional limit theorem for self-normalized partial sum processes in the $M_{1}$ topology. https://arxiv.org/abs/2411.18236

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