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Tanaka Formula for Multidimensional Brownian Motions

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  • H. Uemura

    (Aichi University of Education)

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.

Suggested Citation

  • H. Uemura, 2004. "Tanaka Formula for Multidimensional Brownian Motions," Journal of Theoretical Probability, Springer, vol. 17(2), pages 347-366, April.
    • Handle: RePEc:spr:jotpro:v:17:y:2004:i:2:d:10.1023_b:jotp.0000020698.51262.24
    DOI: 10.1023/B:JOTP.0000020698.51262.24
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    References listed on IDEAS

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    1. Imkeller, Peter & Perez-Abreu, Victor & Vives, Josep, 1995. "Chaos expansions of double intersection local time of Brownian motion in and renormalization," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 1-34, March.
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