Advances in the Projective Dynamics Method: A Procedure of Discretizing the Space applied to Markovian Processes

The projection of a continuous space process to a discrete space process via the transition rates between neighboring bins allows us to relate a master equation to a solution of a stochastic differential equation. The presented method is formulated in its general form for the first time and tested with the Brownian Diffusion process of noninteracting particles with white noise in simple one-dimensional potentials. The comparison of the first passage time obtained with Projective Dynamics, Brownian motion simulations and analytical solutions show the accuracy of this method as well as a wide independence of the particular choice of the binning process.