Non-parametric adaptive estimation of the drift for a jump diffusion process

TL;DR

This paper develops adaptive, non-parametric estimators for the drift function of a jump diffusion process observed discretely, providing risk bounds under ergodic and mixing conditions.

Contribution

It introduces a penalized least-squares method for adaptive drift estimation in jump diffusions with theoretical risk bounds.

Findings

Two adaptive estimators with risk bounds

Effective handling of jump diffusion processes

Theoretical guarantees under ergodic and mixing assumptions

Abstract

In this article, we consider a jump diffusion process (X_t)observed at discrete times t=0,Delta,...,nDelta. The sampling interval Delta tends to 0 and nDelta tends to infinity. We assume that (X_t) is ergodic, strictly stationary and exponentially \beta-mixing. We use a penalized least-square approach to compute two adaptive estimators of the drift function b. We provide bounds for the risks of the two estimators.