A Tanaka formula for the derivative of intersection local time in 1
Abstract
Let Bt be a one dimensional Brownian motion, and let α' denote the derivative of the intersection local time of Bt 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 = ∫0t LsBs - xdBs - ∫0t sgn(Bt - Bu - x) du which was given as a formal identity by Rosen without proof.
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