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Given a standard Brownian motion B, we show that the equation has a unique strong solution X. Here L X is the symmetric local time of X at 0, and β is a given differentiable function with β(0) = 0, −1 < β (·) < 1. (For linear β(·), the solution is the familiar skew Brownian motion).doi:10.1214/ecp.v5-1018 fatcat:aaeixuxhz5bc3p5blpdwgo4doa