Error bounds in stochastic-geometric normal approximation

Mathew Penrose 1 Tom Rosoman 1
1 Department of Mathematical Sciences [Bath]
Abstract : We provide normal approximation error bounds for sums of the form $\sum_x \xi_x$, indexed by the points $x$ of a Poisson process (not necessarily homogeneous) in the unit $d$-cube, with each term $\xi_x$ determined by the configuration of Poisson points near to $x$ in some sense. We consider geometric graphs and coverage processes as examples of our general results.
Keywords : Central limit theorem Berry Essèen bound stochastic geometry coverage process
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Communication dans un congrès
Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.71-94, 2008, DMTCS Proceedings
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Mathew Penrose, Tom Rosoman. Error bounds in stochastic-geometric normal approximation. Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.71-94, 2008, DMTCS Proceedings. 〈hal-01194682〉

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