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Tanaka Formula for Multidimensional Brownian Motions

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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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Authors and Affiliations

  1. Department of Mathematics Education, Aichi University of Education, Kariya, Japan

    H. Uemura

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  1. H. Uemura
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Uemura, H. Tanaka Formula for Multidimensional Brownian Motions. Journal of Theoretical Probability 17, 347–366 (2004). https://doi.org/10.1023/B:JOTP.0000020698.51262.24

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  • DOI: https://doi.org/10.1023/B:JOTP.0000020698.51262.24

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