Statistical estimation and nonlinear filtering in environmental pollution

被引：0
作者：
Qizhu Liang
Jie Xiong
Xingqiu Zhao
机构：
[1] Jinan University,School of Financial Mathematics and Statistics, Guangdong University of Finance
[2] Jinan University,College of Information Science and Technology
[3] Southern University of Science and Technology,Department of Mathematics and SUSTech International Center for Mathematics
[4] The Hong Kong Polytechnic University,Department of Applied Mathematics
来源：
Statistical Inference for Stochastic Processes | 2024年 / 27卷
关键词：
Nonlinear filtering; Stochastic partial differential equation; Optimal filter; Invariant probability measure; Pathwise average distance;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：373 / 390
页数：17
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