Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise

TL;DR

This paper establishes that, under certain smoothness conditions, observing a high-frequency or continuous inhomogeneous jump-diffusion process is asymptotically equivalent to a Gaussian white noise experiment, facilitating analysis and inference.

Contribution

It proves the asymptotic equivalence between jump-diffusion observations and Gaussian white noise models for the drift parameter, with explicit Markov kernels for practical conversion.

Findings

Asymptotic equivalence holds under smoothness conditions on the drift.

Explicit Markov kernels enable transition between models.

Results apply as observation time T tends to infinity.

Abstract

We prove the global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a time inhomogeneous jump-diffusion process and a Gaussian white noise experiment. Here, the considered parameter is the drift function, and we suppose that the observation time $T$ tends to $\infty$. The approximation is given in the sense of the Le Cam $\Delta$-distance, under smoothness conditions on the unknown drift function. These asymptotic equivalences are established by constructing explicit Markov kernels that can be used to reproduce one experiment from the other.