90 research outputs found
Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry
A Poisson or a binomial process on an abstract state space and a symmetric
function acting on -tuples of its points are considered. They induce a
point process on the target space of . The main result is a functional limit
theorem which provides an upper bound for an optimal transportation distance
between the image process and a Poisson process on the target space. The
technical background are a version of Stein's method for Poisson process
approximation, a Glauber dynamics representation for the Poisson process and
the Malliavin formalism. As applications of the main result, error bounds for
approximations of U-statistics by Poisson, compound Poisson and stable random
variables are derived, and examples from stochastic geometry are investigated.Comment: Published at http://dx.doi.org/10.1214/15-AOP1020 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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