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I am working with a problem of the Ito-stochastic differential form given by $$\mathrm{d}x=g(x,t)\,\mathrm{d}t+f(x,t)\,\mathrm{d}W,$$ where $W$ is a Wiener process. I furthermore have to satisfy the condition $$x(t_f)=x_f,$$ where $x_f$ is a constant vector and $t_f$ is the final integration time.

How can I use Mathematica built-in functions to solve this in reverse from $t=t_f$ to $t=0$, such as with RandomFunction?

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  • $\begingroup$ BrownianBridgeProcess lets you pin the process at the ends. Depending on your $g$ and $f$, you might be able to represent the solution in the form of a bridge, or transformed bridge process. $\endgroup$
    – flinty
    Commented Apr 12, 2023 at 20:50
  • $\begingroup$ @flinty thanks. Idk if that will work, but Ill look into that. $\endgroup$
    – JAC
    Commented Apr 14, 2023 at 3:30

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