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A Factorisation of Diffusion Measure and Finite Sample Path Constructions

Author

Listed:
  • Alexandros Beskos

    (University of Warwick)

  • Omiros Papaspiliopoulos

    (Universitat Pompeu Fabra)

  • Gareth O. Roberts

    (University of Warwick)

Abstract

In this paper we introduce decompositions of diffusion measure which are used to construct an algorithm for the exact simulation of diffusion sample paths and of diffusion hitting times of smooth boundaries. We consider general classes of scalar time-inhomogeneous diffusions and certain classes of multivariate diffusions. The methodology presented in this paper is based on a novel construction of the Brownian bridge with known range for its extrema, which is of interest on its own right.

Suggested Citation

  • Alexandros Beskos & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "A Factorisation of Diffusion Measure and Finite Sample Path Constructions," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 85-104, March.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:1:d:10.1007_s11009-007-9060-4
    DOI: 10.1007/s11009-007-9060-4
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    Citations

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    Cited by:

    1. Nan Chen & Zhengyu Huang, 2013. "Localization and Exact Simulation of Brownian Motion-Driven Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 591-616, August.
    2. Wanmo Kang & Jong Mun Lee, 2019. "Unbiased Sensitivity Estimation of One-Dimensional Diffusion Processes," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 334-353, February.
    3. Marcin Mider & Paul A. Jenkins & Murray Pollock & Gareth O. Roberts, 2022. "The Computational Cost of Blocking for Sampling Discretely Observed Diffusions," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3007-3027, December.
    4. Jan Baldeaux, 2011. "Exact Simulation of the 3/2 Model," Papers 1105.3297, arXiv.org, revised May 2011.
    5. Krzysztof Łatuszyński & Gareth O. Roberts, 2013. "CLTs and Asymptotic Variance of Time-Sampled Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 237-247, March.
    6. Murray Pollock, 2015. "On the Exact Simulation of (Jump) Diffusion Bridges," Papers 1505.03030, arXiv.org.
    7. Étoré Pierre & Martinez Miguel, 2013. "Exact simulation of one-dimensional stochastic differential equations involving the local time at zero of the unknown process," Monte Carlo Methods and Applications, De Gruyter, vol. 19(1), pages 41-71, March.
    8. Herrmann, Samuel & Massin, Nicolas, 2023. "Exact simulation of the first passage time through a given level of jump diffusions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 553-576.
    9. Murray Pollock & Paul Fearnhead & Adam M. Johansen & Gareth O. Roberts, 2020. "Quasi‐stationary Monte Carlo and the ScaLE algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1167-1221, December.
    10. Peavoy, Daniel & Franzke, Christian L.E. & Roberts, Gareth O., 2015. "Systematic physics constrained parameter estimation of stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 182-199.
    11. Jan Baldeaux & Eckhard Platen, 2012. "Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods," Papers 1204.1126, arXiv.org.

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