A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of functionals of solution to the SDE and a reconstruction theorem for general stochastic symmetries is proved. Moreover, the notable case of reduction under the closed subclass of quasi Doob transformations is presented. The theoretical results are applied to stochastic models relevant in the applications.

中文翻译：

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通过 Girsanov 和准 Doob 对称性减少和重建 SDE

提出了一种基于包括Girsanov随机变换在内的随机对称性的随机微分方程的约简过程。在这种情况下，给出了一种新的重构概念，涉及 SDE 解泛函的期望值，并证明了一般随机对称性的重构定理。此外，还提出了在准 Doob 变换的封闭子类下减少的显着案例。理论结果应用于应用中相关的随机模型。