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A Tanaka formula for the derivative of intersection local time in $\reals^1$

Greg Markowsky
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Abstract

Let $B_t$ be a one dimensional Brownian motion, and let $α'$ denote the derivative of the intersection local time of $B_t$ as defined in Jay Rosen's work (see references). The object of this paper is to prove the following formula $(1/2)α'_t(x) + (1/2)sgn(x)t = \int_0^t L_s^{B_s - x}dB_s - \int_0^t sgn(B_t - B_u - x) du$ which was given as a formal identity by Rosen without proof.

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Greg Markowsky. 2006-09-04. A Tanaka formula for the derivative of intersection local time in $\reals^1$. https://arxiv.org/abs/math/0609084

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