A Convergent Discretization Method for Transition Path Theory for Diffusion Processes

Transition path theory (TPT) for diffusion processes is a framework analyzing the transitions of multiscale ergodic between disjoint metastable subsets state space. Most methods applying TPT involve construction Markov model on discretization space that approximates underlying process. However, assumption Markovianity difficult to verify in practice, and there are date no known error bounds or convergence results these methods. We propose Monte Carlo method approximating forward committor, probability current, streamlines from processes. Our uses only sample trajectory data partitions based Voronoi tessellations. It does not require Markovian rigorously prove approximate objects use show their exact counterparts limit arbitrarily fine discretization. illustrate some features our by application process solves Smoluchowski equation triple-well potential.