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In this paper we prove the existence and uniqueness of a solution for a one-dimensional quasilinear stochastic differential equation of the Skorohod type, with a non-linear boundary condition of the form . The method of proof uses the Girsanov transformation and some basic exponential estimates. When the coefficients of the equation are deterministic we show that the solution is weakly differentiable on the Wiener space and possesses a continuous modification.
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