Stable convergence of partial sum processes towards discontinuous limits

Johannes Brutsche

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arXiv · 2608.12740

Stable convergence of partial sum processes towards discontinuous limits

Johannes Brutsche

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Abstract

We develop a stable convergence theorem for partial sum processes on sample-size dependent stochastic bases. The result allows multidimensional semimartingale limits that have conditionally independent increments and both a continuous and discontinuous martingale part. Motivated by infill asymptotics, it complements classical Gaussian stable limit theorems and supports applications to likelihood based statistical inference.

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Johannes Brutsche. 2026-08-13. Stable convergence of partial sum processes towards discontinuous limits. https://arxiv.org/abs/2608.12740

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