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arXiv · 2611.04308

Almost sure exponential stability of multi-dimensional stochastic systems driven by a symmetric $α$-stable process

Xuekang Zhang·Hongjian Liu·Guangjun Shen
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Abstract

This article investigates the stability of a class of multidimensional stochastic systems driven by a symmetric $α$-stable process with $1<α<2$. These driving processes have infinite second moments, which prevents the direct application of standard second-moment methods and may lead to divergent jump integrals in the generators of quadratic Lyapunov functions. We establish criteria for $p$th-moment exponential stability and almost sure exponential stability. A numerical example illustrates the theoretical results.

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Xuekang Zhang, Hongjian Liu, Guangjun Shen. 2026-11-03. Almost sure exponential stability of multi-dimensional stochastic systems driven by a symmetric $α$-stable process. https://arxiv.org/abs/2611.04308

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