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PreprintCC BY-NC-ND 4.0arXiv

Stochastic wave equations driven by space-time G-white noise under sublinear expectation

  • Xiaojun Ji
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Abstract

In this paper, we study one-dimensional semilinear stochastic wave equations driven by multiplicative space-time G-white noise under sublinear expectation. We establish the existence and uniqueness of global mild solutions. By developing the quadratic variation structure of space-time G-white noise and establishing a Burkholder-Davis-Gundy inequality for the associated stochastic integrals, we derive higher-order moment estimates and prove the quasi-sure Hölder continuity of the solutions. We further show that the mild solution satisfies the corresponding weak formulation.

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Cite

BibTeXRIS
BibTeX
@misc{ji2026stochastic,
  title = {{Stochastic wave equations driven by space-time $G$-white noise under sublinear expectation}},
  author = {Xiaojun Ji},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07978},
  eprint = {2610.07978},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07978},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Stochastic wave equations driven by space-time G-white noise under sublinear expectation
AU  - Xiaojun Ji
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.07978
UR  - https://arxiv.org/abs/2610.07978
AB  - In this paper, we study one-dimensional semilinear stochastic wave equations driven by multiplicative space-time G-white noise under sublinear expectation. We establish the existence and uniqueness of global mild solutions. By developing the quadratic variation structure of space-time G-white noise and establishing a Burkholder-Davis-Gundy inequality for the associated stochastic integrals, we derive higher-order moment estimates and prove the quasi-sure Hölder continuity of the solutions. We further show that the mild solution satisfies the corresponding weak formulation.
ER  -