A general result on precise asymptotics for linear processes of positively associated sequences

作者：Tan Xi li^*; Yang Xiao yun

来源：Applied Mathematics-A Journal of Chinese Universities Series B, 2008, 23(2): 190-196.

DOI：10.1007/s11766-008-0208-y

• PA sequence
• linear process
• general law
• precise asymptotics

Let {epsilon(t); t is an element of Z(+)} be a strictly stationary sequence of associated random variables with mean zeros, let 0 < E epsilon(2)(1) < infinity and sigma(2) = E epsilon(2)(1) + 2 Sigma(j=2) E epsilon(1)epsilon(j) with 0 < sigma(2) < infinity. {aj; j is an element of Z(+)} is a sequence of real numbers satisfying Sigma(infinity)(j=0) vertical bar a(j)vertical bar < infinity. Define a linear process X(t) = Sigma(infinity)(j=0) a(j)epsilon(t-j), t >= 1, ans S(n) = Sigma(n)(t=1) X(t), n >= 1. Assume that E vertical bar epsilon(1)vertical bar(2+delta ') < infinity for some delta ' > 0 and mu(n) = O(n(-rho)) for some rho > 0. This paper achieves a general law of precise asymptotics for {Sn}.

• 出版日期2008-6
• 单位北华大学; 吉林大学