Probabilities of hitting of shifted small balls by the centered Poisson process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 63-85
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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.
@article{ZNSL_2001_278_a3,
author = {P. Deheuvels and M. A. Lifshits},
title = {Probabilities of hitting of shifted small balls by the centered {Poisson} process},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {63--85},
publisher = {mathdoc},
volume = {278},
year = {2001},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a3/}
}
TY - JOUR AU - P. Deheuvels AU - M. A. Lifshits TI - Probabilities of hitting of shifted small balls by the centered Poisson process JO - Zapiski Nauchnykh Seminarov POMI PY - 2001 SP - 63 EP - 85 VL - 278 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a3/ LA - ru ID - ZNSL_2001_278_a3 ER -
P. Deheuvels; M. A. Lifshits. Probabilities of hitting of shifted small balls by the centered Poisson process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 4, Tome 278 (2001), pp. 63-85. http://geodesic.mathdoc.fr/item/ZNSL_2001_278_a3/