The multiple stochastic integrals and ``nonpoissonian'' transformations of the gamma measure
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 191-220
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We study the transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions for the transformed measure (possible, nonpoissonian) to be absolutely continuous and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use the Poisson analog of the multiple stochastic integral. As an example we consider the transformations of the so-called gamma measure.
@article{ZNSL_2005_328_a11,
author = {N. V. Smorodina},
title = {The multiple stochastic integrals and ``nonpoissonian'' transformations of the gamma measure},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {191--220},
publisher = {mathdoc},
volume = {328},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a11/}
}
TY - JOUR AU - N. V. Smorodina TI - The multiple stochastic integrals and ``nonpoissonian'' transformations of the gamma measure JO - Zapiski Nauchnykh Seminarov POMI PY - 2005 SP - 191 EP - 220 VL - 328 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a11/ LA - ru ID - ZNSL_2005_328_a11 ER -
N. V. Smorodina. The multiple stochastic integrals and ``nonpoissonian'' transformations of the gamma measure. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 9, Tome 328 (2005), pp. 191-220. http://geodesic.mathdoc.fr/item/ZNSL_2005_328_a11/