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

Asymptotic equivalence for inhomogeneous jump diffusion processes and white noise