Lets say I have a Brownian motion process $B_t$ in the interval $[0,T]$.
Is there a known way to sample a particular Brownian motion family from the space of all Brownian motions, for instance - sampling uniformly from the subspace of Brownian motions which satisfy $B_{\text{argmax}} - B_T =d$ for a given $d$. There are more possible properties, and I also have ideas on sampling other stochastic processes, but is there any literature on something similar currently?
The idea is to be able to simulate a sample from that subspace without necessarily knowing the distribution. I know that if you have the distribution the sampling is more straight forward.