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  本文選題：WOD隨機變量　切入點：完全收斂性　出處：《安徽大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：目前,關(guān)于獨立隨機變量在概率極限理論中的研究成果己經(jīng)相對完善,但是在實際情況中,樣本或者變量不一定是獨立的,所以后繼有很多學(xué)者提出了相依結(jié)構(gòu),比如負相協(xié)變量(簡稱NA變量)、負象限相依變量(簡稱NOD變量)、推廣的負象限相依變量(簡稱END變量)以及寬象限相依變量(簡稱WOD變量),其中最廣泛的相依變量就是WOD變量.當(dāng)下,有不少學(xué)者對其進行研究,并取得許多卓有成效的成果,但并不完善.因此對于WOD變量的進一步深入研究具有一定的理論意義以及研究價值.在本文中,首先利用WOD變量的Rosenthal型最大值矩不等式和隨機變量的截尾技術(shù),在一般的條件下建立了WO 變量加權(quán)和的完全收斂性與WOD變量加權(quán)和的最大值序列的完全收斂性,并且給出數(shù)值模擬,驗證了其理論結(jié)果是確實有效的.而完全矩收斂性是一類比完全收斂性更強的收斂性,因此在建立了WOD的完全收斂性的基礎(chǔ)上,進一步研究了WOD序列的完全矩收斂性.所得結(jié)果推廣了若干相依變量的相應(yīng)結(jié)果.本文所建立的WOD變量的完全收斂性和完全矩收斂性的結(jié)果豐富和完善了WO 變量的概率極限理論.
[Abstract]:At present, the research on independent random variables in probability limit theory has been relatively perfect, but in the actual situation, the samples or variables are not necessarily independent, so many scholars have proposed the dependent structure. For example, negative dependent variables (na variables for short), negative quadrant dependent variables (NOD variables for short), generalized negative quadrant dependent variables (END variables) and wide quadrant dependent variables (WOD variables for short) are the most widely dependent variables. A quantity is a WOD variable. Many scholars have studied it, and made many fruitful results, but not perfect. Therefore, the further study of WOD variables has certain theoretical significance and research value. Firstly, by using the Rosenthal type maximum moment inequality of WOD variables and the truncation technique of random variables, the complete convergence of the weighted sum of WO variables and the maximal sequence of weighted sums of WOD variables are established under general conditions. Numerical simulation is given to verify the validity of the theoretical results, and the complete moment convergence is a kind of convergence which is stronger than the complete convergence. Therefore, the complete convergence of WOD is established. In this paper, we further study the complete moment convergence of WOD sequences, and generalize the corresponding results of some dependent variables. The results of complete convergence and complete moment convergence of WOD variables established in this paper enrich and perfect the WO variables. The theory of probability limit.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O211.4

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本文編號：1559998