Statistical Inference for Fractional Diffusions

TL;DR

This paper reviews statistical inference methods for fractional diffusions driven by fractional Brownian motion, discusses theoretical foundations, remaining challenges, and introduces a novel approach, including homogenisation limits.

Contribution

It provides a comprehensive review of existing inference methods, identifies challenges, and proposes a new approach for fractional diffusions.

Findings

Reviewed the theory for defining fractional diffusions.

Identified key challenges in statistical inference for fractional diffusions.

Introduced a novel inference approach and discussed homogenisation limits.

Abstract

This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them. The second section reviews existing theory of statistical inference for fractional diffusions, identifies remaining challenges and introduces a novel approach. The final section discusses results for the case where fractional diffusions result as a homogenisation limit.