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Exact and unbiased simulation of rare events
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Hodgson, James (2022) Exact and unbiased simulation of rare events. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3860967
Abstract
Rare event estimation is the problem of quantifying how unlikely is the occurrence of an event which is already known to be unlikely. Rare event problems are found in many areas of study, including finance, chemistry, biology, and physics (a foundational problem for the field was the neutron shielding problem in physics: how likely is a particle to cross a material barrier without being absorbed or deflected?).
The type of rare event problem this thesis is concerned with is that of determining the probability that a continuous-time Markov process hits a certain known set before a certain stopping time. Numerous algorithms exist for this class of problems, requiring sample paths of the Markov process. Many of these algorithms are known to produce unbiased estimates for the rare event probability, and sometimes considerable effort has been spent to establish that they do so (for example, Br´ehier et al. [2016]).
Many continuous-time Markov processes, such as diffusion processes, must be discretised in time to be simulated on a computer. But usually, access to a complete, continuous sample-path of the process is necessary to determine the course of a rare event algorithm. For the discretised samples which are usually used in practice then, the resulting rare event estimator cannot be guaranteed to be unbiased, although this is rarely acknowledged explicitly.
Recent work in the exact and ε-strong simulation of diffusions, and in unbiased inference for diffusions, seems to suggest solutions to this problem is some contexts. The contribution of this thesis will be to show how this synthesis can be carried out, and investigate the effectiveness of the resulting algorithms.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Markov processes -- Mathematical models, Diffusion processes -- Mathematical models, Algorithms, Approximation theory | ||||
Official Date: | January 2022 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Statistics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Johansen, Adam M. ; Pollock, Murray | ||||
Format of File: | |||||
Extent: | ix, 111 pages : illustrations | ||||
Language: | eng |
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