A Tanaka formula for the derivative of intersection local time in \reals¹

2006/09/04 by Greg Markowsky, Markowsky, Greg
Economics, Econometrics and Finance · Mathematics · #60G17 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G17

paper · pdf · doi:10.48550/arxiv.math/0609084

arxiv created 2006/09/04 · openalex publication_date 2006/09/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 = ∫₀^t L_s^{B_s - x}dB_s - ∫₀^t sgn(B_t - B_u - x) du which was given as a formal identity by Rosen without proof.

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