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PreprintarXiv licencearXiv

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 pth-moment exponential stability and almost sure exponential stability. A numerical example illustrates the theoretical results.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026almost,
  title = {{Almost sure exponential stability of multi-dimensional stochastic systems driven by a symmetric $α$-stable process}},
  author = {Xuekang Zhang and Hongjian Liu and Guangjun Shen},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04308},
  eprint = {2611.04308},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04308},
}
RIS
TY  - UNPB
TI  - Almost sure exponential stability of multi-dimensional stochastic systems driven by a symmetric α-stable process
AU  - Xuekang Zhang
AU  - Hongjian Liu
AU  - Guangjun Shen
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04308
UR  - https://arxiv.org/abs/2611.04308
AB  - 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 pth-moment exponential stability and almost sure exponential stability. A numerical example illustrates the theoretical results.
ER  -