Tanaka Formula for Multidimensional Brownian Motions

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• 作者：H. Uemura
• 关键词：Tanaka formula ; Brownian local time ; Newtonian potential ; Skorohod integral ; Doob– ; Meyer decomposition
• 刊名：Journal of Theoretical Probability
• 出版时间：April, 2004
• 出版年：2004
• 期刊代码：20_08949840
• 类别：eco
• 卷：17
• 期：2
• 页码：347-366
• 数据来源：sp

摘要

We study the Tanaka formula for multidimensional Brownian motions in the framework of generalized Wiener functionals. More precisely, we show that the submartingale U(B_t–x) is decomposed in the sence of generalized Wiener functionals into the sum of a martingale and the Brownian local time, U being twice of the kernel of Newtonian potential and B_t the multidimensional Brownian motion. We also discuss on an aspect of the Tanaka formula for multidimensional Brownian motions as the Doob–Meyer decomposition.