کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1153806 958353 2009 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On Cantrell-Rosalsky's strong laws of large numbers
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آمار و احتمال
پیش نمایش صفحه اول مقاله
On Cantrell-Rosalsky's strong laws of large numbers
چکیده انگلیسی
Starting from a result of almost sure (a.s.) convergence for nonnegative random variables, a simplified proof of a strong law of large numbers (SLLN) established in ([Cantrell, A., Rosalsky, A., 2003. Some strong law of large numbers for Banach space valued summands irrespective of their joint distributions. Stochastic Anal. Appl. 21, 79-95], Theorem 1) for random elements in a real separable Banach space is presented, and some other results of a.s. convergence related to SLLNs in ([Cantrell, A., Rosalsky, A., 2004. A strong law for compactly uniformly integrable sequences of independent random elements in Banach spaces. Bull. Inst. Math. Acad. Sinica 32, 15-33], Th. 3.1) and ([Cantrell, A., Rosalsky, A., 2003. Some strong law of large numbers for Banach space valued summands irrespective of their joint distributions. Stochastic Anal. Appl. 21, 79-95], Theorem 2) are derived. No conditions of independence or on the joint distribution of random elements are required. Likewise, no geometric condition on the Banach space where random elements take values is imposed. Some applications to weighted (for an array of constants) sums of random elements and to the case of random sets are also considered.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Statistics & Probability Letters - Volume 79, Issue 6, 15 March 2009, Pages 842-847
نویسندگان
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