Before revision:  When the diffusion coefficient is locally Holder continuous with some exponent in (0, 1], the stochastic solution  is shown to be a classical solution . A comparison theorem for the Cauchy problem is also proved, without the\ge  linear growth condition on the diffusion coefficient.
After revision:  When the diffusion coefficient is locally Holder continuous with some exponent in (0, 1], the stochastic solution is shown to be a classical solution to the Cauchy problem is also proved, without the\ge linear growth condition on the diffusion coefficient.