Abstract
We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance for a large class of geometric functionals of marked Poisson and binomial point processes on general metric spaces. The rates are valid whenever the geometric functional is expressible as a sum of exponentially stabilizing score functions satisfying a moment condition. By incorporating stabilization methods into the Malliavin–Stein theory, we obtain rates of normal approximation for sums of stabilizing score functions which either improve upon existing rates or are the first of their kind.
Our general rates hold for functionals of marked input on spaces more general than full-dimensional subsets of
Citation
Raphaël Lachièze-Rey. Matthias Schulte. J. E. Yukich. "Normal approximation for stabilizing functionals." Ann. Appl. Probab. 29 (2) 931 - 993, April 2019. https://doi.org/10.1214/18-AAP1405
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