Nonparametric estimation of trend for SDEs with delay driven by fractional Brownian motion with small noise

TL;DR

This paper develops a kernel-based nonparametric method to estimate the trend in stochastic delay differential equations driven by fractional Brownian motion, focusing on small noise scenarios.

Contribution

It introduces a novel kernel-type estimation approach tailored for SDEs with delay and fractional noise, expanding nonparametric estimation techniques.

Findings

Effective kernel estimator for the trend in fractional SDEs with delay

Theoretical properties of the estimator established

Simulation results demonstrate estimator accuracy

Abstract

We investigate the problem of nonparametric estimation of the trend for stochastic differential equations with delay and driven by a fractional Brownian motion through the method of kernel-type estimation for the estimation of a probability density function.