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PreprintCC BY 4.0arXiv

Generalized Wishart processes under nonlinear expectation

  • Xinpeng Li
  • Yiran Mi
  • Jian Song
  • Shuzhen Yang
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Abstract

We develop a theory of generalized Wishart processes within the framework of G-expectation, with G-Dyson Brownian motion and the G-Wishart process as two typical examples. In contrast to the classical setting, we show that G-Dyson Brownian motion may exhibit collisions and provide a sufficient condition ensuring the non-collision of the eigenvalues of generalized Wishart processes. We then derive the equations governing the high-dimensional limits of the empirical spectral measures under G-expectation, leading to the corresponding semicircle law for G-Dyson Brownian motion and Marchenko--Pastur law for the G-Wishart process.

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Cite

BibTeXRIS
BibTeX
@misc{li2026generalized,
  title = {{Generalized Wishart processes under nonlinear expectation}},
  author = {Xinpeng Li and Yiran Mi and Jian Song and Shuzhen Yang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02728},
  eprint = {2611.02728},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02728},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Generalized Wishart processes under nonlinear expectation
AU  - Xinpeng Li
AU  - Yiran Mi
AU  - Jian Song
AU  - Shuzhen Yang
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02728
UR  - https://arxiv.org/abs/2611.02728
AB  - We develop a theory of generalized Wishart processes within the framework of G-expectation, with G-Dyson Brownian motion and the G-Wishart process as two typical examples. In contrast to the classical setting, we show that G-Dyson Brownian motion may exhibit collisions and provide a sufficient condition ensuring the non-collision of the eigenvalues of generalized Wishart processes. We then derive the equations governing the high-dimensional limits of the empirical spectral measures under G-expectation, leading to the corresponding semicircle law for G-Dyson Brownian motion and Marchenko--Pastur law for the G-Wishart process.
ER  -