论文标题
标量自主ito随机微分方程的对称分类，具有简单的噪声
Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise
论文作者
论文摘要
众所周知，对标量ITO随机微分方程的对称性的知识得益于Kozlov替代，因此导致其整合。在本文中，我们提供了标量自主ito随机微分方程的分类，并具有简单的噪声具有对称性。在这里，“简单噪声”表示噪声系数为$ \ s（x，t）= s x^k $，带有$ s $和$ k $真实常数。这样的方程可以通过众所周知的转换为标准形式。对于此类标准形式，我们还提供对称方程的集成。我们的工作扩展了以前的分类，因为它还考虑了最近引入的类型的对称性，特别是标准的随机对称性，而不是在其中考虑。
It is known that knowledge of a symmetry of a scalar Ito stochastic differential equations leads, thanks to the Kozlov substitution, to its integration. In the present paper we provide a classification of scalar autonomous Ito stochastic differential equations with simple noise possessing symmetries; here "simple noise" means the noise coefficient is of the form $\s (x,t) = s x^k$, with $s$ and $k$ real constants. Such equations can be taken to a standard form via a well known transformation; for such standard forms we also provide the integration of the symmetric equations. Our work extends previous classifications in that it also consider recently introduced types of symmetries, in particular standard random symmetries, not considered in those.
