SIAM review. Society for Industrial and Applied Mathematics. 2018;60(4):909-938. doi: 10.1137/16M1104329 Q110.82024

Trajectory stratification of stochastic dynamics

随机动力学的轨迹分类法翻译改进

Aaron R Dinner^{1 2}, Jonathan C Mattingly³, Jeremy O B Tempkin^{1 2}, Brian Van Koten⁴, Jonathan Weare^{1 4}

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作者单位

¹ James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.

² Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA.

³ Departments of Mathematics and Statistical Science, Duke University, Durham, North Carolina 27708, USA.

⁴ Department of Statistics, The University of Chicago, Chicago, Illinois 60637, USA.

DOI: 10.1137/16M1104329 PMID: 34650314

摘要 Ai翻译

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：stochastic dynamics; trajectory stratification

关键词：随机动力学; 轨迹分层

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期刊名：Siam review

缩写：SIAM REV

ISSN：0036-1445

e-ISSN：1095-7200

IF/分区：10.8/Q1

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