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Stochastic ordinary and partial differential equations generalize the concepts of ordinary and partial differential equations to the setting where the unknown is a stochastic process.

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Phase space Brownian bridge

I understand the concept of the 1 dimensional Brownian bridge with the form of: $$dx_t=\frac{-1}{1-t}x_t \, dt + dw_t$$ s.t. $x_0=0$ and $x_1=0$ where $dw_t$ is a Wiener process. I am thinking about t …