U-statistics in stochastic geometry

  title={U-statistics in stochastic geometry},
  author={Rapha{\"e}l Lachi{\`e}ze-Rey and Matthias Reitzner},
A U-statistic of order k with kernel f : X →Rd over a Poisson process is defined in [25] as ∑ x1,...,xk∈η 6= f (x1, . . . ,xk) under appropriate integrability assumptions on f . U-statistics play an important role in stochastic geometry since many interesting functionals can be written as Ustatistics, like intrinsic volumes of intersection processes, characteristics of random geometric graphs, volumes of random simplices, and many others, see for instance [15, 18, 25]. It turns out that the… CONTINUE READING