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Interacting particle approximations of Feynman-Kac measures for continuous-time jump processes
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Angeli, Letizia (2020) Interacting particle approximations of Feynman-Kac measures for continuous-time jump processes. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3518295~S15
Abstract
The cloning algorithm has been introduced in the theoretical physics literature as a numerical procedure to study the large deviations of additive path functionals of stochastic processes. Due to its broad applicability, the convergence properties of the cloning algorithm have recently become a subject of research interest with only partial progress in continuous time. In this work, we derive rigorous convergence results by providing a novel interpretation of the cloning algorithm based on Feynman-Kac models and their particle approximations. We then adapt already established convergence results for mean field particle approximations to a broader class of interacting particle approximations, which includes cloning algorithms. This way, we obtain bias and L p error bounds, with order of convergence given respectively by 1/N and 1/ √ N, and a Central Limit Theorem. Finally, we show how to apply these results to the study of large deviations of additive path functionals for Markov processes and, in particular, how to construct efficient interacting particle approximations for estimating the scaled cumulant generating function. Our results apply to a vast class of jump processes on locally compact state spaces, and do not involve any time discretization in contrast to previous approaches. This also provides a rigorous framework that can be used to explore the various degrees of freedom in the design of interacting particle approximations and to improve the efficiency of the algorithms.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Jump processes, Differential equations, Partial, Stochastic processes, Clones (Algebra) | ||||
Official Date: | September 2020 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Sponsors: | Grosskinsky, Stefan ; Johansen, Adam M. | ||||
Format of File: | |||||
Extent: | v, 107 leaves : colour illustrations | ||||
Language: | eng |
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