Dependent Limit Theory Of Random Variables Results

Limit theory is one of the key branches of Probability theory, and also the important foundation of other branches. The research purpose about recent Limit theory is to weaken the restrictions of "independence" and to customize them to reality for easier identification and application. But considered their complexity , enormous problems has not been fingered out. In this paper, some problems are studied and some results are obtained as follows based on analyzing their characters.1. Given some probability exponential inequalities of maximal partial sums for sequences of NQD random variables, some Laws of Logarithm and Laws of the Iterated Logarithm for Nonidentity Pairwise NQD Sequences are obtained. Some results of literature become into particular case of our results and be improved.2. In this chapter, Marciewicz- Zygmund Strong Laws for weighted sums of(ρ|～)-mixing sequences are investigated by firstly establishing the Bernstain Inequalityfor weighed sums of p -mixing sequences. The results extend and greatly improvethe corresponding results of literature.3. Aimed at more wider Mimesis-Weighted Function and Cricital Function, some precise asymptotic properties are obtained for U-statistics made up of random variables from Attraction District a Stable Distribution. And two following corollaries are gained for U-statistics made up of random variables from Attraction District of Normal Distribution.