Precise Asymptotics In The Complete Moment Convergence For ?~- Mixing Random Variables Sequence And Linear Process Generated By ?~- Mixing Random Variables Sequence

Probability theory is a science of quantitative law of random phenomena,which is extensively applied in natural science,managerial science,economic and finance etc.due to the universality of random phenomena.Limit theory is not one of the main branches of probability,but also an essential theoretical foundation of other fields of probability theory and mathematical statistics.As the important content of probability theory,the study of precise asymptotics is a hot research direction all the time.In this thesis,we mainly research on the precise asymptotics of the logarithm law in the com-plete moment convergence,which about partial sum under suitable conditions for ?-mixing random sequences and linear process generated by linearly positively quadrant dependent sequence.In chapter 2,we study the precise asymptotics of the logarithm law in the complete moment convergence,which about partial sum under suitable conditions for ?-mixing random sequences.In chapter 3,we extend the results of chapter 2 to linear process,and further s-tudy the precise asymptotics of the complete moment convergence for linear process generated by ?-mixing random sequence.