Parameter estimation in diagonalizable bilinear stochastic parabolic equations

TL;DR

This paper addresses parameter estimation in stochastic parabolic equations with multiplicative noise, revealing singularities that enable improved estimators and the development of exact closed-form solutions.

Contribution

It introduces a novel approach exploiting singularities in the estimation problem to enhance convergence rates and construct exact estimators for stochastic parabolic equations.

Findings

Improved convergence rates for estimators.

Existence of a closed-form exact estimator.

Singularity exploited for better estimation.

Abstract

A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion processes. From the point of view of classical statistics, this problem turns out to be singular not only for the original infinite-dimensional system but also for most finite-dimensional projections. This singularity can be exploited to improve the rate of convergence of traditional estimators as well as to construct completely new closed-form exact estimator.