black and inside $B_\beta$ in grey. Each time the trajectory in one cell attempts to exit the cell, the exit point position (depicted as an open circle) is stored, and used to reinitialize the trajectory into the neighboring cell. []{data-label="fig:voronoi"}](fig1){width="3in"}

If we were to generate an infinitely long trajectory of the system, $\zz(t)$ with $t>0$, this trajectory would keep going in and out of the cells $B_\alpha$ by crossing the edges between these cells. Out of this trajectory we could therefore generate an ensemble of exit-entry points, i.e. those points on the edges of the cells at which the trajectory goes from a cell $B_\alpha$ into a neighboring cell $B_{\beta}$. By the Markovian assumption, these points are all we need to generate an exact sample of trajectories inside each of the cells $B_\alpha$ simply by starting trajectories at the points leading into that cell and running these trajectories forward in time until they exit the cell. The procedure in Refs.  is a way to generate these pieces of trajectories inside the cells without having to compute the entry points beforehand from a long unbiased trajectory but rather by generating them on-the-fly. To understand how this is done, imagine that we 