Almost Sure Central Limit Theorem And Complete Moment Convergence Rate

Probabilistic limit theory is not only one of the main branches of probability theory,but also an important theoretical basis of other branches of probability theory and mathematical statistics.Its research results have been widely used in natural science,engineering,biology,finance and other fields.Probabilistic limit theory One of the research directions is almost everywhere central limit theorem,and the classical almost everywhere central limit theorem is the limit theorem of logarithmic weighted forms.Many scholars at home and abroad have studied the limit properties of the central limit theorem,the law of large numbers and the complete convergence of the random variable sequence.However,the research results of almost all the central limit theorems of weighted sums are not perfect.Fu Yanli(2011)gives the almost everywhere central limit theorem of the product of the sum of the sum of the strong mixing sequence.In the first chapter,we use the central limit theorem and the moment inequality of the mixed sequence weighted sum to improve its weight and get better the result of.Probabilistic limit theory is another research direction is accurate asymptotic,and the exact asymptotic nature of moment convergence is a major research content.With many independent random variable sequence,or dependent random variable sequence,many scholars have made in-depth And some scholars have generalized the mixed sequence to the linear process of the mixed sequence.Liu Jun et al.(2008)give the exact asymptotic behavior of the linear convergence of the strong mixing sequence,and the second chapter uses the strong mixing sequence The weak convergence theorem and the moment inequality of the generated linear process are extended to the moment of complete convergence.