Geodesic
Small ball probability for centered Poisson process of high intensity
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 280-303

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We study the limiting behavior of the probability with which the path of a centered Poisson process of high intensity gets into a small ball with a receding center. The results of this paper are restricted to the simplest case where the variation of the shift function (center of the ball) is finite. The estimates are obtained under the optimal conditions for the intensity of the process. 
@article{ZNSL_2003_298_a16,
     author = {E. Yu. Shmileva},
     title = {Small ball probability for centered {Poisson} process of high intensity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {280--303},
     publisher = {mathdoc},
     volume = {298},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a16/}
}
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E. Yu. Shmileva. Small ball probability for centered Poisson process of high intensity. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 6, Tome 298 (2003), pp. 280-303. http://geodesic.mathdoc.fr/item/ZNSL_2003_298_a16/