Mixed Limit The Nature Of The Dependent Variable

This thesis is finished under the guidance of my tutor, professor Lin Zhengyan, during my master of science. It consists of three chapters:Chapter 1 Several convergence theorems for arrays of rowwiseρ*-mixing random variablesSince Bradley put forward the concept ofρ*-mixing random variables in 1990, its convergence properties have drawn many attentions from scholars for its extensive applications. But the weak law of large numbers and the complete convergence for arrays of rowwiseρ*-mixing random variables have not been reported. This chapter discusses these contents, only under the condition ofρ*(1) < 1, without any restriction of the mixing rate, we get:Theorem 0.1.1 Let {Xnk; 1 ≤ k≤ n, n ≥ 1} be an array of rowwiseρ*-mixing random variables withρ*(1) < 1. For any 0 < p < 2, and any n ≥ 1, there exist some constants M > 0 and δ > 0 such that max . ThenwhereTheorem 0.1.2 Let be an array of rowwiseρ*-mixing random variables withρ*(l) < 1. For any 0 < p < 1, and any n ≥ 1, there exist some constants M > 0 and δ > 0 such that max . ThenwhereTheorem 0.1.3 Let be an array of rowwisep*-mixing random variables withρ*(l) < 1. For any 1 < p < r < 2, and any n > 1, there exist some constants M > 0 and 0 < δ < 2 - r/p such that max . Thenwhere...