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(Bt−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 Bt 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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