Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Tanaka formula for the derivative of intersection local time in
  $\reals^1$   Let $B_t$ be a one dimensional Brownian motion, and let $\alpha'$ 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 $(1/2)\alpha'_t(x) + (1/2)sgn(x)t = \int_0^t L_s^{B_s - x}dB_s -
\int_0^t sgn(B_t - B_u - x) du$ which was given as a formal identity by Rosen
without proof.

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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: econ