次线性期望下随机变量序列的收敛性与一致可积性
发布时间：2018-10-16 10:37
【摘要】：本文主要讨论次线性期望空间(Ω,H,E)中随机变量序列的收敛性、一致可积性和一致不可积性,并证明一些新的结果.首先介绍次线性期望空间中随机变量序列几种收敛的定义和它们之间的关系,在次线性期望具有单调连续性的假设下证明了LP收敛比依容度收敛要强,依容度收敛比依分布收敛要强,并给出了依分布收敛的一些刻画.其次介绍了次线性期望空间中随机变量序列一致可积的定义,并证明了一致可积的充要条件.最后,对比经典概率空间情形给出次线性期望空间中随机变量序列一致不可积的定义,并给出了一些刻画.
[Abstract]:In this paper, we discuss the convergence, uniform integrability and uniform non-integrability of random variable sequences in sublinear expected spaces (惟, Hwe E), and prove some new results. This paper first introduces the definitions of the convergence of random variable sequences in the sublinear expectation space and their relations. Under the assumption that the sublinear expectation has monotone continuity, it is proved that the convergence of LP is stronger than the convergence of tolerance. Convergence by tolerance is stronger than that by distribution, and some characterizations of convergence by distribution are given. Secondly, the definition of uniformly integrable sequence of random variables in sublinear expected space is introduced, and the necessary and sufficient conditions for uniformly integrable sequence are proved. Finally, the uniformly non-integrable definition of the sequence of random variables in the sublinear expected space is given, and some characterizations are given.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.5
，
本文编号：2274093
[Abstract]:In this paper, we discuss the convergence, uniform integrability and uniform non-integrability of random variable sequences in sublinear expected spaces (惟, Hwe E), and prove some new results. This paper first introduces the definitions of the convergence of random variable sequences in the sublinear expectation space and their relations. Under the assumption that the sublinear expectation has monotone continuity, it is proved that the convergence of LP is stronger than the convergence of tolerance. Convergence by tolerance is stronger than that by distribution, and some characterizations of convergence by distribution are given. Secondly, the definition of uniformly integrable sequence of random variables in sublinear expected space is introduced, and the necessary and sufficient conditions for uniformly integrable sequence are proved. Finally, the uniformly non-integrable definition of the sequence of random variables in the sublinear expected space is given, and some characterizations are given.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.5
，
本文编号：2274093
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