Complete Moment Convergence For The Widely Orthant Dependent Linear Processes With Random Coefficients

On the one hand,it is well known that probability limit theory is an important branch of probability theory,and also the fundamental of probability and statistics theory.It focuses on the studies of convergence,rates of convergence for various random variables and so on.Due to the need of practical application,scholars' attention has shifted from the probability limit theory of independent random variables to random variables under various dependent structures and mixed structures.Particularly the widely orthant dependent structures which include many dependent structures have more extensive prospects in application.On the other hand,the properties and asymptotic behaviors of linear processes(infinite moving average processes)are studied in many applied fields such as electronics,financial mathematics and time series force their significant influences,particular the more widespread application of the linear processes with random coefficients.Based on widely orthant dependent structures,the paper first talks conditions which random coefficients need to satisfy in order to obtain the moment inequality and maximal moment inequality of linear processes.Secondly,the paper focuses on the complete moment convergence and rate of complete moment convergence for the sum and maximal sum of linear processes with random coefficients under the condition of random domination.Further the paper obtains corresponding results of complete convergence and rate of complete convergence in corollaries.In a word,the results in the paper generalize recent researches in the area in some way,and have more widespread application.