Parametric Estimation for Processes Driven by Infinite Dimensional Mixed Fractional Brownian Motion

TL;DR

This paper investigates parametric estimation techniques for stochastic processes driven by infinite dimensional mixed fractional Brownian motion, extending previous work on fractional Brownian motion to more complex infinite-dimensional settings.

Contribution

It introduces new methods for parametric estimation specifically tailored for processes driven by infinite dimensional mixed fractional Brownian motion, filling a gap in existing research.

Findings

Developed estimation procedures for infinite dimensional mixed fractional Brownian motion

Extended existing fractional Brownian motion estimation techniques to infinite dimensions

Provided theoretical analysis of the proposed estimation methods

Abstract

Parametric and nonparametric inference for stochastic processes driven by a fractional Brownian motion were investigated in Mishura (2008) and Prakasa Rao(2010) among others. Similar problems for processes driven by an infinite dimensional fractional Brownian motion were studied in Prakasa Rao (2004,2013), Cialenco (2009) and others. Parametric estimation for processes driven by infinite dimensional mixed fractional Brownian motion is discussed in this article.