The Limit Theorem Of Two Types Of Process

The limit theorem which researches the asymptotic behavior of a sequence of random variablesplays an important role in the probability theory. What describe the rate of convergence moreprecisely in the limit theorem is the large deviation, the moderate deviation and the law of theiterated logarithm. So the paper studies the limit theorem of two types of process from thesetwo aspects respectively. Specifically including two parts, on one hand we study the moderatedeviation of a sequence of negatively associated random variables, on the other hand we study thelaw of the iterated logarithm of the signal process.In chapter1, we mainly review the conceptes of the heavy tailed random variables and neg-atively associated random variables. Giving a few common heavy-tailed distribution classes, wediscuss their relation. Finally, we discuss the properties of negatively associated random variables.In chapter2, we research the moderate deviation of a sequence of negatively associated randomvariables which belong to the dominated variation class. First, we get the result of the moderatedeviation of the part sum, then, on the basis of which, we get the moderate of the random sum.In chapter3, we prove that the least-square estimator of the parameter in the signal processmeets the law of the iterated logarithm, and we get the inequalities for probabilities of the largedeviation.