Rare Event Simulation for Stochastic Dynamics in Continuous Time

• Published in: Journal of statistical physics Vol. 176; no. 5; pp. 1185 - 1210
• Main Authors: Angeli, Letizia, Grosskinsky, Stefan, Johansen, Adam M., Pizzoferrato, Andrea
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-09-2019; Springer; Springer Nature B.V
• Subjects: Algorithms; Cloning; Computer simulation; Convergence; Mathematical and Computational Physics; Monte Carlo method; Monte Carlo simulation; Physical Chemistry; Physics; Physics and Astronomy; Quantum Physics; Statistical Physics and Dynamical Systems; Theoretical; Sequential Monte Carlo; Cloning algorithm; Interacting particle systems; Dynamic large deviations
• ISSN: 0022-4715; 1572-9613
• DOI: 10.1007/s10955-019-02340-1

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.