Probabilities of hitting of shifted small balls by the centered Poisson process

We investigate the probabilities of hitting shifted small balls by sample paths of centered Poisson process and find the exact range of parameters where Wiener approximation of those probabilities is valid. Towards this aim, we introduce the Skorokhod density technique which, for the Poisson process, plays a role similar to that of the Cameron–Martin formula in construction of associated laws for Gaussian measure.