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Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions - Part II: Numerical Approach in Continuous Time | | Esteban Guevara Hidalgo
; Takahiro Nemoto
; Vivien Lecomte
; | | Date: |
29 Jul 2016 | | 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. | | Source: | arXiv, 1607.8804 | | Services: | Forum | Review | PDF | Favorites | |
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