Inference for SDEs driven by Hermite processes

TL;DR

This paper develops estimators for parameters of nonlinear stochastic differential equations driven by Hermite processes, using weighted quadratic variations, and proves their weak consistency from discrete observations.

Contribution

It introduces new estimators for the Hurst parameter, Hermite order, and noise intensity in SDEs driven by Hermite processes, with proven consistency.

Findings

Estimators are consistent under in-fill asymptotics.

Method applies to nonlinear SDEs with Hermite noise.

Provides theoretical foundation for parameter inference in complex stochastic models.

Abstract

In the paper, we address parametric and non-parametric estimation for nonlinear stochastic differential equations with additive Hermite noise with possibly nonlinear scaling. We assume that a single trajectory of the solution is observed discretely and we propose estimators of the Hurst parameter and the Hermite order of the driving process as well as of the average noise intensity and noise intensity function. The estimators are based on the weighted quadratic variation whose properties are used, in particular, to prove weak consistency of the proposed estimators under in-fill asymptotics.