A Convergent Discretization Method for Transition Path Theory for Diffusion Processes
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Publication:5857920
DOI10.1137/20M1329354zbMATH Open1457.34095arXiv1907.05799OpenAlexW3015052221WikidataQ124353289 ScholiaQ124353289MaRDI QIDQ5857920
Author name not available (Why is that?)
Publication date: 8 April 2021
Published in: (Search for Journal in Brave)
Abstract: Transition path theory (TPT) for diffusion processes is a framework for analysing the transitions of multiscale ergodic diffusion processes between disjoint metastable subsets of state space. Most methods for applying TPT involve the construction of a Markov state model on a discretisation of state space that approximates the underlying diffusion process. However, the assumption of Markovianity is difficult to verify in practice, and there are to date no known error bounds or convergence results for these methods. We propose a Monte Carlo method for approximating the forward committor, probability current, and streamlines from TPT for diffusion processes. Our method uses only sample trajectory data and partitions of state space based on Voronoi tessellations. It does not require the construction of a Markovian approximating process. We rigorously prove error bounds for the approximate TPT objects and use these bounds to show convergence to their exact counterparts in the limit of arbitrarily fine discretisation. We illustrate some features of our method by application to a process that solves the Smoluchowski equation on a triple-well potential.
Full work available at URL: https://arxiv.org/abs/1907.05799
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