Convergence Rates in the Law of Large Numbers for Arrays of Martingale Differences

大数定律中鞅差阵列的收敛速度(英文版)

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Author: Hao Shunli
Language: English
ISBN/ISSN: 9787563732425
Published on: 2015-11
Soft Cover

《大数定律中鞅差阵列的收敛速度(英文版)》属于鞅极限理论，主要内容建立在作者郝顺利近年来发表的三篇SCI科研论文和近期的一些新科研成果的基础上。作者主要研究实值和Banach值鞅差阵列在大数定律中的收敛速度，从四个方向推广著名的Baum—Katz定理，也从多个侧面推广和改进许宝騄（1948年当选为中央研究院院士，1955年当选为中国科学院学部委员）和tterbert Robbins、Paul Erdos（1983—1984年的沃尔夫奖获得者）、周元燊（1974年当选为中央研究院第十届院士）和Tze Leung Lai、Gerold Alsmeyer等著名数学家的相关主要成果，并推广了相关领域内众多新成果。法国知名教授Alain Rouault说这些结果是原创的，法国的另一位教授Thomas Duquesne认为这些结果是完美的。

0 Preliminary knowledge
0.1 Probability spaces， random variables and random elements
0.2 Expectation and conditional expectation
0.3 Martingale
0.4 Slowly varing function
1 C.R.s of R—valued m.d.s
1.1 Maximal inequalities for martingales
1.2 C.R.s for arrays of m.d.s
1.3 C.R.s for triangular arrays of m.d.s
1.4 C.R.s for the maxima of any r.v.s
1.5 C.R.s for martingales
1.6 C.R.s for specially weighted sums of m，d.s
1.7 Extention to supermartingales
2 C.R.s of B—valued m.d.s
2.1 Maximal inequalities for martingales
2.2 C.R.s for arrays of m.d.s
2.3 C.R.s for triangular arrays of m.d.s
2.4 C.R.s for the maxima of any r.e.s
2.5 C.R.s for martingales
2.6 C.R.s for specially weighted sums of m.d.s
2.7 C.R.s for generally weighted sums of m.d.s
2.7.1 Law of large numbers for weighted sums of m.d.s
2.7.2 Complete convergence of weighted sums of m.d.s
3 C.R.s for randomly weighted sums of m.d.s
3.1 Main results
3.2 Preliminaries
3.3 Proofs of the main results
Bibliography
Index