# Statistical Analysis of Some Evolution Equations Driven by Space-only Noise

## TL;DR

This paper investigates the statistical properties and estimation methods for stochastic evolution equations driven by space-only noise, highlighting new inverse problem approaches and estimator properties.

## Contribution

It introduces novel estimators for drift and diffusion coefficients in space-only noise driven equations and analyzes their properties, addressing a gap in inverse problem research.

## Key findings

- Derived multiple estimators for model coefficients
- Proved properties of the estimators
- Explored the interplay between classical and non-traditional models

## Abstract

We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations have been studied, little is known about inverse problems for these equations. We exploit the somewhat unusual structure of the observations coming from these equations that leads to an interesting interplay between classical and non-traditional statistical models. We derive several types of estimators for the drift and/or diffusion coefficients of these equations, and prove their relevant properties.