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数学进展 - 2018, Vol. 47(2): 243-258
研究论文
基于$G$-布朗运动的泛函Itô公式
Functional Itô's Formula for $G$}-Brownian Motion

李小娟1,王法磊2
LI Xiaojuan1,*, WANG Falei2

1. 山东青年政治学院信息工程学院, 济南, 山东, 250103;
2. 山东大学中泰证券金融研究院, 济南, 山东, 250100
1. School of Information Engineering, Shandong Youth University of Political Science, Jinan, Shandong, 250103, P. R. China;
2. Zhongtai Securities Institute of Finance, Shandong University, Jinan, Shandong, 250100, P. R. China

收稿日期: 2016-06-06
出版日期: 2018-05-16
2018, Vol. 47(2): 243-258
DOI: 10.11845/sxjz.2016073b


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摘要 本文用Dupire轨道导数作为工具, 得到了基于$G$-布朗运动的泛函Itô公式. 应用此泛函Itô公式, 建立了全非线性的泛函Feynman-Kac公式.
关键词 $G$-期望$G$-布朗运动轨道导数泛函Feynman-Kac公式    
Abstract:In this paper, we obtain the functional Itô's formula for $G$-Brownian motion by the Dupire's path-derivatives. As an application, we establish the fully nonlinear functional Feynman-Kac formula.
Key words$G$-expectation    $G$-Brownian motion    path derivative    functional Feynman-Kac formula
PACS:  O211.6  
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