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Any suggestion on solving the stochastic differential equation

\begin{align} dW(t) = d\widetilde{W}(t) + \left(\frac{\kappa - W(t)}{\tau-t} - \frac{1}{\kappa - W(t)}\right)dt \end{align}

where $\kappa,\tau\in\mathbb{R}$ are known and $\widetilde{W}(t)$ is a standard Brownian motion and $W(t)$ a Gaussian process ?

I tried looking this equation as a bridge, but it is not a bridge.

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