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Statistical estimation and nonlinear filtering in environmental pollution

Author

Listed:
  • Qizhu Liang

    (Jinan University
    Jinan University)

  • Jie Xiong

    (Southern University of Science and Technology)

  • Xingqiu Zhao

    (The Hong Kong Polytechnic University)

Abstract

Motivated by the water pollution detection, this paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated, which indicates the concentration of undesired chemical in a river, is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly consistent estimators of unknown parameters are derived at first. With the optimal filter given by Bayes formula, the uniqueness of invariant measure for the signal-filter pair has been verified. The paper then establishes approximation to the optimal filter with estimators, showing that the pathwise average distance, per unit time, of the computed approximating filter from the optimal filter converges to zero in probability. Simulation results are presented at last.

Suggested Citation

  • Qizhu Liang & Jie Xiong & Xingqiu Zhao, 2024. "Statistical estimation and nonlinear filtering in environmental pollution," Statistical Inference for Stochastic Processes, Springer, vol. 27(2), pages 373-390, July.
    • Handle: RePEc:spr:sistpr:v:27:y:2024:i:2:d:10.1007_s11203-023-09303-0
    DOI: 10.1007/s11203-023-09303-0
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    References listed on IDEAS

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    1. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704, Decembrie.
    2. Brigo, Damiano & Hanzon, Bernard, 1998. "On some filtering problems arising in mathematical finance," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 53-64, May.
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