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Multilevel estimation of expected exit times and other functionals of stopped diffusions

Abstract:
This paper proposes and analyzes a new multilevel Monte Carlo method for the estimation of mean exit times for multidimensional Brownian diffusions and associated functionals which correspond to solutions to high-dimensional parabolic PDEs through the Feynman–Kac formula. In particular, it is proved that the complexity to achieve an ε root-mean-square error is O(ε −2 |log ε| 3 ).
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1137/17M1116660

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Hughs College
ORCID:
0000-0002-5445-3721
Publisher:
Society for Industrial and Applied Mathematics Publisher's website
Journal:
SIAM/ASA Journal on Uncertainty Quantification Journal website
Volume:
6
Issue:
4
Pages:
1454–1474
Publication date:
2018-10-18
Acceptance date:
2018-08-13
DOI:
ISSN:
2166-2525
Pubs id:
pubs:911573
URN:
uri:2e414828-0bdd-4c7c-b88c-c9600a3094ad
UUID:
uuid:2e414828-0bdd-4c7c-b88c-c9600a3094ad
Local pid:
pubs:911573

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