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.