For technical reasons, it becomes necessary to do the following: instead of looking  seconds into the "future", and considering the limit as , one "rewinds" the noise  seconds into the "past", and evolves the system through  seconds using the same initial condition.
Due to technical constraints, we must alter our approach. Instead of predicting future events based on a given timeframe, we will rewind the noise for  seconds into the past and then evolve the system over  seconds using the same starting conditions.