Tanaka Formula for Multidimensional Brownian Motions |
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| Authors: | H Uemura |
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| Institution: | (1) Department of Mathematics Education, Aichi University of Education, Kariya, Japan |
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| Abstract: | 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. |
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| Keywords: | Tanaka formula Brownian local time Newtonian potential Skorohod integral Doob– Meyer decomposition |
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