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Non-nested Adaptive Timesteps in Multilevel Monte Carlo Computations

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 163)

Abstract

This paper shows that it is relatively easy to incorporate adaptive timesteps into multilevel Monte Carlo simulations without violating the telescoping sum on which multilevel Monte Carlo is based. The numerical approach is presented for both SDEs and continuous-time Markov processes. Numerical experiments are given for each, with the full code available for those who are interested in seeing the implementation details.

Keywords

  • multilevel Monte Carlo
  • adaptive timestep
  • SDE
  • continuous-time Markov process

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Acknowledgments

MBG’s research was funded in part by EPSRC grant EP/H05183X/1, and CL and JW were funded in part by a CCoE grant from NVIDIA. In compliance with EPSRC’s open access initiative, the data in this paper, and the MATLAB codes which generated it, are available from doi:10.5287/bodleian:s4655j04n. This work has benefitted from extensive discussions with Ruth Baker, Endre Süli, Kit Yates and Shenghan Ye.

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Correspondence to Michael B. Giles .

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Giles, M.B., Lester, C., Whittle, J. (2016). Non-nested Adaptive Timesteps in Multilevel Monte Carlo Computations. In: Cools, R., Nuyens, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods. Springer Proceedings in Mathematics & Statistics, vol 163. Springer, Cham. https://doi.org/10.1007/978-3-319-33507-0_14

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