کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4608707 | 1338374 | 2013 | 27 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Probabilistic diophantine approximation and the distribution of Halton–Kronecker sequences
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Probabilistic diophantine approximation and the distribution of Halton–Kronecker sequences Probabilistic diophantine approximation and the distribution of Halton–Kronecker sequences](/preview/png/4608707.png)
چکیده انگلیسی
By a Halton–Kronecker sequence we mean a sequence in the s+ts+t-dimensional unit-cube which is the combination of an ss-dimensional Halton sequence and a tt-dimensional Kronecker sequence ({n⋅α})n=0,1,… with α∈Rt. The investigation of such ‘hybrid sequences’ for their use in Monte Carlo and quasi-Monte Carlo methods first was motivated by Spanier (1995) [20]. By suitably adapting techniques of Jozsef Beck on probabilistic diophantine approximation, developed in Beck (1994) [2], we can show that for almost all α∈Rt for the discrepancy DNDN of a Halton–Kronecker sequence we have DN=O((logN)s+t+ϵN) for all ϵ>0ϵ>0, which most probably essentially is the best possible metrical result for this type of sequences.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 29, Issue 6, December 2013, Pages 397–423
Journal: Journal of Complexity - Volume 29, Issue 6, December 2013, Pages 397–423
نویسندگان
Gerhard Larcher,