Rare event simulation for stochastic dynamics in continuous time

Abstract

Large deviations for additive path functionals of stochastic dynamics and related numerical approaches have attracted significant recent research interest. We focus on the question of convergence properties for cloning algorithms in continuous time, and establish connections to the literature of particle filters and sequential Monte Carlo methods. This enables us to derive rigorous convergence bounds for cloning algorithms which we report in this paper, with details of proofs given in a further publication. The tilted generator characterizing the large deviation rate function can be associated to non-linear processes which give rise to several representations of the dynamics and additional freedom for associated numerical approximations. We discuss these choices in detail, and combine insights from the filtering literature and cloning algorithms to compare different approaches and improve efficiency.

33 pages, 3 figures

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• Fluctuation theorems for stochastic dynamics
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Duality and hidden symmetries in interacting particle systems
• A numerical approach to large deviations in continuous-time
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Cited by in corpus (5)

• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Sampling rare events across dynamical phase transitions
• Efficient large deviation estimation based on importance sampling
• Limit theorems for cloning algorithms
• Adaptive power method for estimating large deviations in Markov chains