Finite-Time and -Size Scalings in the Evaluation of Large Deviation Functions: 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 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.

arXiv comment12 pages, 10 figures. Second part of pair of companion papers, following Part I arXiv:1607.04752

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• Sampling rare events across dynamical phase transitions
• Finite time large deviations via matrix product states
• Weighted ensemble: Recent mathematical developments
• Large deviations and optimal control forces for hard particles in one dimension
• Efficient characterisation of large deviations using population dynamics
• A large deviation theory perspective on nanoscale transport phenomena
• Rare event simulation for stochastic dynamics in continuous time
• Approaching a large deviation theory for complex systems
• Limit theorems for cloning algorithms
• Dynamical phase transitions for the activity biased Ising model in a magnetic field
• Breakdown of the Finite-Time and -Population Scalings of the Large Deviation Function in the Large-Size Limit of a Contact Process
• Non-Markovian feedback control and acausality: an experimental study
• Computing large deviation rate functions of entropy production for diffusion processes by an interacting particle method