@article{b98dc3729a3b415f9dc29845c9e0a0b1,
title = "Trajectory stratification of stochastic dynamics",
abstract = "We present a general mathematical framework for trajectory stratification for simulating rare events. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of state space (strata), computing averages over the distributions of the trajectory fragments within the strata with minimal communication between them, and combining those averages with appropriate weights to yield averages with respect to the original underlying process. Our framework reveals the full generality and flexibility of trajectory stratification, and it illuminates a common mathematical structure shared by existing algorithms for sampling rare events. We demonstrate the power of the framework by defining strata in terms of both points in time and path-dependent variables for efficiently estimating averages that were not previously tractable.",
keywords = "Computational statistical mechanics, Molecular dynamics, Monte Carlo methods, Rare events",
author = "Dinner, {Aaron R.} and Mattingly, {Jonathan C.} and Tempkin, {Jeremy O.B.} and {Van Koten}, Brian and Jonathan Weare",
note = "Funding Information: \ast Received by the editors November 21, 2016; accepted for publication (in revised form) October 16, 2017; published electronically November 8, 2018. http://www.siam.org/journals/sirev/60-4/M110432.html Funding: This work was supported by the National Institute of Health (NIH), grant 5 R01 GM109455-02. The work of the third author was supported by the NSF Graduate Research Fellowship Program. Computational resources were provided by the University of Chicago Research Computing Center (RCC). \dagger James Franck Institute and Department of Chemistry, The University of Chicago, Chicago, IL 60637 (dinner@uchicago.edu). \ddagger Departments of Mathematics and Statistical Science, Duke University, Durham, NC 27708 (jonm@math.duke.edu). \S James Franck Institute and Department of Chemistry, The University of Chicago, Chicago, IL 60637 (jtempkin@uchicago.edu). \P Department of Statistics, The University of Chicago, Chicago, IL 60637 (bvankoten@gmail.com). \| James Franck Institute and Department of Statistics, The University of Chicago, Chicago, IL 60637 (weare@uchicago.edu). Publisher Copyright: {\textcopyright} 2018 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license",
year = "2018",
doi = "10.1137/16M1104329",
language = "English (US)",
volume = "60",
pages = "909--938",
journal = "SIAM Review",
issn = "0036-1445",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "4",
}