Statistical Estimation and Nonlinear Filtering in Environmental Pollution

TL;DR

This paper addresses nonlinear filtering for environmental pollution models, deriving consistent parameter estimators, proving filter uniqueness, and demonstrating convergence of approximations through simulations.

Contribution

It introduces new methods for parameter estimation and filter approximation in nonlinear stochastic PDE models of pollution.

Findings

Consistent estimators for unknown parameters are derived.

Uniqueness of the invariant measure for the signal-filter pair is established.

Approximate filters converge to the optimal filter in probability.

Abstract

This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly consistent estimators of the 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, 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.