Abstract In this work, we develop polynomial processes where the coefficients of the process may depend on time. A full characterization of this model class is given by means of their semimartingale characteristics. While in the time-homogeneous case, moments can be calculated easily through matrix exponentials, we show that in the inhomogeneous case this is no longer possible. As an alternative we explore a connection to Magnus series for fast numerical approximations. The model class studied in this work extends existing models, for example Sato processes and time-inhomogeneous affine processes.

中文翻译：

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时间非齐次多项式过程

摘要 在这项工作中，我们开发了多项式过程，其中过程的系数可能取决于时间。该模型类的完整特征通过其半鞅特征给出。虽然在时间齐次的情况下，矩可以通过矩阵指数轻松计算，但我们表明，在非齐次的情况下，这不再可能。作为替代方案，我们探索了与马格努斯级数的联系以实现快速数值近似。在这项工作中研究的模型类扩展了现有模型，例如佐藤过程和时间非均匀仿射过程。