Weighted Random Variables And The Limits Of Nature

This thesis is finished under the guidance of my tutor, Professor Su Zhonggen . It consists of four chapters: In Chapter 1 we will study the weighted sums of the linear NQD random sequence, and prove that the strong law of large numbers still holds for the linear NQD random sequence . The results can be regarded as the generalization of the case of i.i.d random variables sequence . In Chapter 2 we will study the φ-mixing random sequence and obtain its limiting behaviour mentioned in Chen pingyan (2002), and obtain the Chover's law of the iterated logarithm (LIL) for the partial sums of the sequence discussed in this chapter. In Chapter 3 we will generalize the results of Chapter 2 and obtain the similar limiting results. At last, we will give a brief review of the ruin porobability related stoch astic process, and some remarks and open problems are presented.