On fixed points of Poisson shot noise transforms

@misc{citeulike:2967860, abstract = {Distributional fixed points of a Poisson shot noise transform (for nonnegative, nonincreasing response functions bounded by 1) are characterized. The tail behavior of fixed points is described. Typically they have either exponential moments or their tails are proportional to a power function, with exponent greater than -1. The uniqueness of fixed points is also discussed. Finally, it is proved that in most cases fixed points are absolutely continuous, apart from the possible atom at zero.}, author = {Iksanov, Aleksander M. and Jurek, Zbigniew J. }, citeulike-article-id = {2967860}, eprint = {math/0209015}, keywords = {poisson, probability, probability-course}, month = {Feb}, posted-at = {2008-07-06 21:28:54}, priority = {2}, title = {On fixed points of Poisson shot noise transforms}, url = {http://arxiv.org/abs/math/0209015}, year = {2003} }

TY - ELEC ID - citeulike:2967860 L3 - citeulike-article-id:2967860 TI - On fixed points of Poisson shot noise transforms N2 - Distributional fixed points of a Poisson shot noise transform (for nonnegative, nonincreasing response functions bounded by 1) are characterized. The tail behavior of fixed points is described. Typically they have either exponential moments or their tails are proportional to a power function, with exponent greater than -1. The uniqueness of fixed points is also discussed. Finally, it is proved that in most cases fixed points are absolutely continuous, apart from the possible atom at zero. KW - poisson KW - probability KW - probability-course AU - Iksanov, Aleksander AU - Jurek, Zbigniew PY - 2003/Feb/16/ UR - http://arxiv.org/abs/math/0209015 ER -