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

TL;DR

This paper introduces a numerical method leveraging finite-time and finite-size scalings to improve the estimation of large deviation functions in stochastic systems, demonstrated on the contact process.

Contribution

The proposed approach enhances the accuracy of large deviation function estimators by systematically accounting for finite-time and finite-size effects.

Findings

Improved estimators for large deviation functions using finite-scaling methods

Application to the contact process shows significant accuracy gains

Method reduces finite-simulation biases in rare trajectory sampling

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 provides a numerical tool allowing their study, by means of simulating a large number of copies of the system, which are subjected to selection rules that favor 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 paper, we present a numerical approach which uses the finite-time and finite-size scalings of estimators of the large deviation functions associated to the distribution of rare trajectories. The method we propose allows one to extract the infinite-time and infinite-size limit of these estimators which -- as shown on the contact process -- provides a significant improvement of the large deviation functions estimators compared to the the standard one.