Abstract We give a new definition of a Levy driven CARMA random field, defining it as a generalized solution of a stochastic partial differential equation (SPDE). Furthermore, we give sufficient conditions for the existence of a mild solution of our SPDE. Our model unifies all known definitions of CARMA random fields, and in particular for dimension 1 we obtain the classical CARMA process.

中文翻译：

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Lévy 驱动的 CARMA 广义过程和随机偏微分方程

摘要 我们给出了 Levy 驱动的 CARMA 随机场的新定义，将其定义为随机偏微分方程 (SPDE) 的广义解。此外，我们给出了 SPDE 温和解存在的充分条件。我们的模型统一了 CARMA 随机场的所有已知定义，特别是对于维度 1，我们获得了经典的 CARMA 过程。