We show that the classical stochastic motion of an open bosonic string leads
to the same results as the standard first quantization of this system. For
this, the diffusion constant governing the process has to be proportional to
\alpha ', the Regge slope parameter, which is the only constant, along with the
velocity of light, needed to describe the motion of a string.Comment: Submitted to Phys. Rev. D, 9 pages RevTex, reference removed, no
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