Mean exit times and the multilevel Monte Carlo method
Higham, Desmond and Mao, Xuerong and Roj, Mikolaj and Song, Qingshuo and Yin, George (2013) Mean exit times and the multilevel Monte Carlo method. SIAM/ASA Journal on Uncertainty Quantification (JUQ), 1 (1). pp. 2-18. (https://doi.org/10.1137/120883803)
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Abstract
Numerical methods for stochastic differential equations are relatively inefficient when used to approximate mean exit times. In particular, although the basic Euler–Maruyama method has weak order equal to one for approximating the expected value of the solution, the order reduces to one half when it is used in a straightforward manner to approximate the mean value of a (stopped) exit time. Consequently, the widely used standard approach of combining an Euler–Maruyama discretization with a Monte Carlo simulation leads to a computationally expensive procedure. In this work, we show that the multilevel approach developed by Giles [Oper. Res., 56 (2008), pp. 607–617] can be adapted to the mean exit time context. In order to justify the algorithm, we analyze the strong error of the discretization method in terms of its ability to approximate the exit time. We then show that the resulting multilevel algorithm improves the expected computational complexity by an order of magnitude, in terms of the required accuracy. Numerical results are provided to illustrate the analysis.
ORCID iDs
Higham, Desmond ORCID: https://orcid.org/0000-0002-6635-3461, Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864, Roj, Mikolaj, Song, Qingshuo and Yin, George;-
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Item type: Article ID code: 44165 Dates: DateEvent27 March 2013PublishedSubjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 20 Jun 2013 09:12 Last modified: 05 Sep 2024 00:45 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/44165