But in more situations the random variables generating counting processes may not independent identically distributed , and in all kinds of dependent relations , negative association ( na ) and positive association ( pa ) are commonly seen . the research and apply in this aspect are rather valuable . in chap 2 we prove wald inequalities and fundamental renewal theorems of renewal counting processes generated by na sequences and pa sequences ; in chap 3 we are enlightened by cheng and wang [ 8 ] , extend some results in gut and steinebach [ 7 ] , obtain the precise asymptotics for renewal counting processes and depict the convergence rate and limit value of renewal counting processes precisely ; at last , in the study of na sequences , su , zhao and wang ( 1996 ) [ 9 ] , lin ( 1997 ) [ 10 ] have proved the weak convergence for partial sums of stong stationary na sequences . however product sums are the generalization of partial sums and also the special condition of more general u - statistic
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