On a Projection Least Squares Estimator for Jump Diffusion Processes

TL;DR

This paper introduces a projection least squares estimator for the drift function of jump diffusion processes, providing theoretical risk bounds and demonstrating its effectiveness through numerical experiments.

Contribution

It presents a novel projection least squares estimator for jump diffusion drift functions, with established risk bounds and adaptive estimation techniques.

Findings

Risk bounds for the estimator are derived.

The estimator performs well in numerical experiments.

Adaptive estimation improves accuracy.

Abstract

This paper deals with a projection least squares estimator of the drift function of a jump diffusion process $X$ computed from multiple independent copies of $X$ observed on $[0,T]$. Risk bounds are established on this estimator and on an associated adaptive estimator. Finally, some numerical experiments are provided.