Parameter estimations for SPDEs with multiplicative fractional noise

TL;DR

This paper investigates parameter estimation methods for diagonalizable SPDEs driven by multiplicative fractional noise, introducing a new class of closed-form exact estimators and applying the results to stochastic heat equations with fractional Brownian motion.

Contribution

It introduces a novel class of closed-form exact estimators for SPDEs with fractional noise, extending the existing estimation techniques to any Hurst parameter.

Findings

Analysis of maximum likelihood estimators for SPDEs with fractional noise.

Development and validation of closed-form exact estimators.

Application of methods to stochastic heat equations with fractional Brownian motion.

Abstract

We study parameter estimation problem for diagonalizable stochastic partial differential equations driven by a multiplicative fractional noise with any Hurst parameter $H\in(0,1)$. Two classes of estimators are investigated: traditional maximum likelihood type estimators, and a new class called closed-form exact estimators. Finally the general results are applied to stochastic heat equation driven by a fractional Brownian motion.