Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
I just want to see is there any interesting form of $\alpha_t$ to link two points $[x_0,v_0]$ and $[x_1,v_1]$ meanwhile it preserves some property (i.e Brownian Bridge is the solution of OT with dirac mass).
