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Reverse-time diffusion equation models

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  • Anderson, Brian D.O.

Abstract

Reverse-time stochastic diffusion equation models are defined and it is shown how most processes defined via a forward-time or conventional diffusion equation model have an associated reverse-time model.

Suggested Citation

  • Anderson, Brian D.O., 1982. "Reverse-time diffusion equation models," Stochastic Processes and their Applications, Elsevier, vol. 12(3), pages 313-326, May.
    • Handle: RePEc:eee:spapps:v:12:y:1982:i:3:p:313-326
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    Citations

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    Cited by:

    1. T. Pellegrino & P. Sabino, 2015. "Enhancing Least Squares Monte Carlo with diffusion bridges: an application to energy facilities," Quantitative Finance, Taylor & Francis Journals, vol. 15(5), pages 761-772, May.
    2. Tang, Han & Yang, Xiangfeng, 2021. "Uncertain chemical reaction equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Zhuohan Wang & Carmine Ventre, 2024. "A Financial Time Series Denoiser Based on Diffusion Model," Papers 2409.02138, arXiv.org.
    4. Prodanov, Dimiter, 2021. "The Burgers equations and the Born rule," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    6. Andrew Lesniewski & Giulio Trigila, 2024. "Beyond Monte Carlo: Harnessing Diffusion Models to Simulate Financial Market Dynamics," Papers 2412.00036, arXiv.org, revised Feb 2025.
    7. Xiaolong Wang & Zhijian He & Xiaojiang Peng, 2024. "Artificial-Intelligence-Generated Content with Diffusion Models: A Literature Review," Mathematics, MDPI, vol. 12(7), pages 1-28, March.
    8. Kardaras, Constantinos & Robertson, Scott, 2017. "Continuous-time perpetuities and time reversal of diffusions," LSE Research Online Documents on Economics 67495, London School of Economics and Political Science, LSE Library.
    9. Minshuo Chen & Renyuan Xu & Yumin Xu & Ruixun Zhang, 2025. "Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure," Papers 2504.06566, arXiv.org, revised Jul 2025.
    10. Constantinos Kardaras & Scott Robertson, 2017. "Continuous-time perpetuities and time reversal of diffusions," Finance and Stochastics, Springer, vol. 21(1), pages 65-110, January.

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