Consider the following SDE with $X_0 = 1$, $$ dX_t = X_t\operatorname{sign}(X_t) \, dt + X_t \, dW_t, $$ where $\operatorname{sign}(x) = \mathbb{1}\{x \ge 0\}$. How am I supposed to solve this SDE?
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gmvh
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