Small Ball Probabilities for a Shifted Poisson Process

We investigate the probabilities of hitting shifted small balls by sample paths of a centered Poisson process and find the exact range of parameters for which the Wiener approximation of these probabilities is valid. Towards this aim, we introduce the Skorokhod density technique. For the Poisson process, this technique plays a role similar to that of the Cameron-Martin formula in the construction of associated laws for a Gaussian measure. Bibliography: 20 titles.