Abstract We consider nonlinear stochastic wave equations driven by time-space white noise. The existence of solutions is proved by the method of successive approximations. Next we apply Newton’s method. The main result concerning its first-order convergence is based on Cairoli’s maximal inequalities for two-parameter martingales. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

中文翻译：

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非线性随机波动方程的牛顿法

摘要 我们考虑由时空白噪声驱动的非线性随机波动方程。解的存在性是通过逐次逼近的方法证明的。接下来我们应用牛顿法。关于其一阶收敛的主要结果是基于 Cairoli 对二参数鞅的最大不等式。此外，证明了概率意义上的二阶收敛。