  This paper establishes the global asymptotic equivalence between a Poisson
process with variable intensity and white noise with drift under sharp
smoothness conditions on the unknown function. This equivalence is also
extended to density estimation models by Poissonization. The asymptotic
equivalences are established by constructing explicit equivalence mappings. The
impact of such asymptotic equivalence results is that an investigation in one
of these nonparametric models automatically yields asymptotically analogous
results in the other models.
