Foundations of an anti-symmetric version of Malliavin calculus

这个项目旨在为反对称版本的Malliavin微积分提供基础。作为输出，我们获得了以下数学结果。首先，我们成功地得到了Kp族的tau函数的一个概率表示，这充分推广了KdV-One上的结果。第二，我们在Wiener空间上构造了Clifford代数的一个表示。在此基础上，我们还成功地构建了概率玻色化，这是我们在这个项目中的第三个主要贡献。除此之外，我们还得到了数学金融中KdV方程孤子与利率期限结构之间关系的一个有趣的结果。

This project aimed to provide foundations to an anti-symmetric version of Malliavin calculus. As outputs, we obtained the following mathematical results. The first is that we have succeeded to obtain a probabilistic representation of tau functions of KP hierarchy, which fully extends the previous results on KdV one. The second is that we constructed a representation of Clifford algebra on Wiener space. Based on it, we also succeeded to construct a probabilistic Bosonization, which is the third of our main contributions in this project. Other than these, we have also obtained an interesting result on a relation between solitons of KdV equation and the term structure of interest rates in mathematical finance.