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arXiv · 2610.07978

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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Xiaojun Ji. 2026-10-06. Stochastic wave equations driven by space-time $G$-white noise under sublinear expectation. https://arxiv.org/abs/2610.07978

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