Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions Part II: Numerical Approach in Continuous Time

Abstract : Rare trajectories of stochastic systems are important to understand – because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provide a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to a selection rule that favors the rare trajectories of interest. Such algorithms are plagued by finite simulation time-and finite population size-effects that can render their use delicate. In this second part of our study (which follows a companion paper [ arXiv:1607.04752 ] dedicated to an analytical study), we present a numerical approach which verifies and uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of the rare trajectories. Using the continuous-time cloning algorithm, we propose a method aimed at extracting the infinite-time and infinite-size limits of the estimator of such large deviation functions in a simple system, where, by comparing the numerical results to exact analytical ones, we demonstrate the practical efficiency of our proposed approach.
Type de document :
Pré-publication, Document de travail
12 pages, 11 figures. Second part of pair of companion papers, following Part I arXiv:1607.04752. 2016
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01350894
Contributeur : Vivien Lecomte <>
Soumis le : mardi 2 août 2016 - 10:46:17
Dernière modification le : mardi 30 mai 2017 - 01:07:51
Document(s) archivé(s) le : mardi 8 novembre 2016 - 21:52:50

Fichiers

ARTICLE_9b.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01350894, version 1
  • ARXIV : 1607.08804

Collections

Citation

Esteban Guevara Hidalgo, Takahiro Nemoto, Vivien Lecomte. Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions Part II: Numerical Approach in Continuous Time. 12 pages, 11 figures. Second part of pair of companion papers, following Part I arXiv:1607.04752. 2016. <hal-01350894>

Partager

Métriques

Consultations de
la notice

147

Téléchargements du document

150