Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise

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.