论文标题
具有多个噪声的可集成ITO方程
Integrable Ito equations with multiple noises
论文作者
论文摘要
标量ITO方程与单个噪声源的分类，该噪声源承认所谓的标准对称性，因此 - 通过Kozlov构造 - 现在已经完成了。在本文中，我们研究了存在两个独立噪声源的物理和生物应用中发生的情况。我们确定所有这样的自主iTO方程都承认标准对称性；然后，我们通过Kozlov构造将它们整合在一起。我们还考虑了三个或更多独立噪声的情况，表明没有标准对称性。
The classification of scalar Ito equations with a single noise source which admit a so called standard symmetry and hence are -- by the Kozlov construction -- integrable is by now complete. In this paper we study the situation, occurring in physical as well as biological applications, where there are two independent noise sources. We determine all such autonomous Ito equations admitting a standard symmetry; we then integrate them by means of the Kozlov construction. We also consider the case of three or more independent noises, showing no standard symmetry is present.
