کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1155686 | 958757 | 2012 | 25 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The scaling limit of Poisson-driven order statistics with applications in geometric probability
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
60H0760D05Random polytopes60G5562G3260F17U-statistics - U آمارOrder statistics - آمار سفارشGeometric probability - احتمال هندسیExtreme values - ارزشهای شدیدprimary - اولیهsecondary - ثانویMalliavin calculus - حساب MalliavinLimit theorems - محدودیت قضیهScaling limit - محدودیت پوسته پوسته شدنIntegral geometry - هندسه انتگرالStochastic geometry - هندسه تصادفی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The scaling limit of Poisson-driven order statistics with applications in geometric probability The scaling limit of Poisson-driven order statistics with applications in geometric probability](/preview/png/1155686.png)
چکیده انگلیسی
Let ηt be a Poisson point process of intensity tâ¥1 on some state space Y and let f be a non-negative symmetric function on Yk for some kâ¥1. Applying f to all k-tuples of distinct points of ηt generates a point process ξt on the positive real half-axis. The scaling limit of ξt as t tends to infinity is shown to be a Poisson point process with explicitly known intensity measure. From this, a limit theorem for the m-th smallest point of ξt is concluded. This is strengthened by providing a rate of convergence. The technical background includes Wiener-Itô chaos decompositions and the Malliavin calculus of variations on the Poisson space as well as the Chen-Stein method for Poisson approximation. The general result is accompanied by a number of examples from geometric probability and stochastic geometry, such as k-flats, random polytopes, random geometric graphs and random simplices. They are obtained by combining the general limit theorem with tools from convex and integral geometry.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 122, Issue 12, December 2012, Pages 4096-4120
Journal: Stochastic Processes and their Applications - Volume 122, Issue 12, December 2012, Pages 4096-4120
نویسندگان
Matthias Schulte, Christoph Thäle,