Tanaka Formula for Multidimensional Brownian Motions

H. Uemura ()
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H. Uemura: Aichi University of Education

Journal of Theoretical Probability, 2004, vol. 17, issue 2, 347-366

Abstract: 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.

Keywords: Tanaka formula; Brownian local time; Newtonian potential; Skorohod integral; Doob–Meyer decomposition (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTP.0000020698.51262.24

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