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Conditioning diffusions with respect to incomplete observations

Author

Listed:
  • Bernard Delyon

    (Univ Rennes
    Institut Agro)

  • Jean-Louis Marchand

    (Univ Rennes
    Institut Agro)

Abstract

In this paper, we prove a result of equivalence in law between a diffusion conditioned with respect to partial observations and an auxiliary process. By partial observations we mean coordinates (or linear transformation) of the process at a finite collection of deterministic times. Apart from the theoretical interest, this result allows to simulate the conditional diffusion through Monte Carlo methods, using the fact that the auxiliary process is easy to simulate.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:3:d:10.1007_s11203-023-09287-x
    DOI: 10.1007/s11203-023-09287-x
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    References listed on IDEAS

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    1. 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.
    2. Gilles Daniel & Nathan Joseph & David Bree, 2005. "Stochastic volatility and the goodness-of-fit of the Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 199-211.
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