What is the Stochastic Differential Equation associated with $X_t = \frac{1}{t+W_t}$ where $W_t$ is a Wiener Process?

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What is the Stochastic Differential Equation associated with $X_t = \frac{1}{t+W_t}$ where $W_t$ is a Wiener Process? I have tried to apply Ito's Formula here, but there is a discontinuity at $0$. Does anyone have any ideas?