We consider a L\'evy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a semilinear one-dimensional stochastic heat equation driven by the space-time white noise.

中文翻译：

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来自 Lévy 表的复杂布朗表的弱逼近及其对 SPDE 的应用

我们考虑平面中的 L\'evy 过程，并使用它来构造一个复值随机场族，我们证明这些随机场在连续函数空间中在法律上收敛到一个复布朗表。我们应用这个结果来获得由时空白噪声驱动的半线性一维随机热方程的随机场解的弱近似。