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Limit theorems for cloning algorithms

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Angeli, Letizia, Grosskinsky, Stefan and Johansen, Adam M. (2021) Limit theorems for cloning algorithms. Stochastic Processes and their Applications, 138 . pp. 117-152. doi:10.1016/j.spa.2021.04.007 ISSN 0304-4149.

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Official URL: https://doi.org/10.1016/j.spa.2021.04.007

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Abstract

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical ‘cloning’ algorithms have been developed to estimate the scaled cumulant generating function, based on importance sampling via cloning of rare event trajectories. So far, attempts to study the convergence properties of these algorithms in continuous time have led to only partial results for particular cases. Adapting previous results from the literature of particle filters and sequential Monte Carlo methods, we establish a first comprehensive and fully rigorous approach to bound systematic and random errors of cloning algorithms in continuous time. To this end we develop a method to compare different algorithms for particular classes of observables, based on the martingale characterization of stochastic processes. Our results apply to a large class of jump processes on compact state space, and do not involve any time discretization in contrast to previous approaches. This provides a robust and rigorous framework that can also be used to evaluate and improve the efficiency of algorithms.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Algorithms, Stochastic processes -- Mathematical models, Limit theorems (Probability theory), Path integrals
Journal or Publication Title: Stochastic Processes and their Applications
Publisher: Elsevier Science BV
ISSN: 0304-4149
Official Date: August 2021
Dates:
DateEvent
August 2021Published
22 April 2021Available
16 April 2021Accepted
Volume: 138
Page Range: pp. 117-152
DOI: 10.1016/j.spa.2021.04.007
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 20 April 2021
Date of first compliant Open Access: 19 August 2021
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/N510129/1Alan Turing Institutehttp://dx.doi.org/10.13039/100012338
EP/R034710/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
EP/T004134/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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