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Simulation of conditioned diffusion and application to parameter estimation

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  • Delyon, Bernard
  • Hu, Ying

Abstract

In this paper, we propose some algorithms for the simulation of the distribution of certain diffusions conditioned on a terminal point. We prove that the conditional distribution is absolutely continuous with respect to the distribution of another diffusion which is easy for simulation, and the formula for the density is given explicitly. An example of parameter estimation for a Duffing-Van der Pol oscillator is given as an application.

Suggested Citation

  • Delyon, Bernard & Hu, Ying, 2006. "Simulation of conditioned diffusion and application to parameter estimation," Stochastic Processes and their Applications, Elsevier, vol. 116(11), pages 1660-1675, November.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:11:p:1660-1675
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    Citations

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    Cited by:

    1. Golightly Andrew & Wilkinson Darren J., 2015. "Bayesian inference for Markov jump processes with informative observations," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(2), pages 169-188, April.
    2. Stefan Sommer, 2019. "An Infinitesimal Probabilistic Model for Principal Component Analysis of Manifold Valued Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 37-62, February.
    3. Golightly, A. & Wilkinson, D.J., 2008. "Bayesian inference for nonlinear multivariate diffusion models observed with error," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1674-1693, January.
    4. Mogens Bladt & Samuel Finch & Michael Sørensen, 2016. "Simulation of multivariate diffusion bridges," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 343-369, March.
    5. 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.
    6. Bernard Delyon & Jean-Louis Marchand, 2023. "Conditioning diffusions with respect to incomplete observations," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 499-523, October.

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