2013 Fiscal Year Final Research Report

Foundations of an anti-symmetric version of Malliavin calculus

Research Project

Project/Area Number	23654056
Research Category	Grant-in-Aid for Challenging Exploratory Research
Allocation Type	Multi-year Fund
Research Field	Basic analysis
Research Institution	Ritsumeikan University
Principal Investigator	AKAHORI Jiro 立命館大学, 理工学部, 教授 (50309100)
Project Period (FY)	2011 – 2013
Keywords	反対称マリアバン解析 / クリフォード代数 / フェルミオン / ボゾン化 / タウ関数
Research Abstract	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.

(5 results)