【摘要】：本文主要討論次線性期望空間(Ω,H,E)中隨機變量序列的收斂性、一致可積性和一致不可積性,并證明一些新的結(jié)果.首先介紹次線性期望空間中隨機變量序列幾種收斂的定義和它們之間的關(guān)系,在次線性期望具有單調(diào)連續(xù)性的假設(shè)下證明了LP收斂比依容度收斂要強,依容度收斂比依分布收斂要強,并給出了依分布收斂的一些刻畫.其次介紹了次線性期望空間中隨機變量序列一致可積的定義,并證明了一致可積的充要條件.最后,對比經(jīng)典概率空間情形給出次線性期望空間中隨機變量序列一致不可積的定義,并給出了一些刻畫.
[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.
【學位授予單位】：南京大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O211.5
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本文編號：2274093