发表机构
Research Center for Mathematics and Interdisciplinary Sciences, Shandong University; Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University（山东大学数学与交叉科学研究中心; 山东大学非线性预期前沿科学中心（教育部））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在次线性期望下研究乘性时空$G$-白噪声驱动的一维半线性随机波动方程，建立了全局温和解的存在唯一性，并证明了高阶矩估计、拟必然Hölder连续性及弱形式满足性。
AI 中文摘要
本文在次线性期望框架下研究由乘性时空$G$-白噪声驱动的一维半线性随机波动方程。我们建立了全局温和解的存在唯一性。通过发展时空$G$-白噪声的二次变差结构，并建立相关随机积分的Burkholder-Davis-Gundy不等式，我们推导出高阶矩估计，并证明了解的拟必然Hölder连续性。我们进一步表明该温和解满足相应的弱形式。
英文摘要
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.
