کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
7549672 1489887 2014 5 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Rate of Poisson approximation for nearest neighbor counts in large-dimensional Poisson point processes
ترجمه فارسی عنوان
نرخ تقریب پواسون برای نزدیکترین شمارش معکوس در فرآیند نقطه پواسون بزرگ بعدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آمار و احتمال
چکیده انگلیسی
Consider two independent homogeneous Poisson point processes Π of intensity λ and Π′ of intensity λ′ in d-dimensional Euclidean space. Let qk,d, k=0,1,…, be the fraction of Π-points which are the nearest Π-neighbor of precisely k   Π′-points. It is known that as d→∞, the qk,d converge to the Poisson probabilities e−λ′/λ(λ′/λ)k/k!, k=0,1,…. We derive the (sharp) rate of convergence d−1/2(4/33)d, which is related to the asymptotic behavior of the variance of the volume of the typical cell of the Poisson-Voronoi tessellation generated by Π. An extension to the case involving more than two independent Poisson point processes is also considered.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 92, September 2014, Pages 143-147
نویسندگان
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